https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/v/simple-quadratic-equation 2021-06-30T17:32:39Z Solving quadratics by taking square roots Sal solves the equation 2x^2+3=75 by isolating x^2 and taking the square root of both sides. Sal Khan video https://cdn.kastatic.org/googleusercontent/yWf29VjN1FQyCVokHPAvjyr7a49zpl9CWatyRRkUZmB2zeD4FK1Wl2yQYP9qLuoOAphF_b7DlchY4U2B7ZdIyBYf Solving quadratics by taking square roots Sal solves the equation 2x^2+3=75 by isolating x^2 and taking the square root of both sides. https://cdn.kastatic.org/ka-youtube-converted/RweAgQwLdMs.mp4/RweAgQwLdMs.mp4 138 Quadratic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/a/solving-quadratic-equations-by-taking-square-roots 2021-12-16T15:37:07.463764128Z Solving quadratics by taking square roots Learn how to solve quadratic equations like x^2=36 or (x-2)^2=49. article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/e/solve-quadratics-by-taking-square-roots-intro 2021-07-08T21:56:39Z Quadratics by taking square roots (intro) Solve simple quadratic equations by taking the square root of both sides of the equation. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/v/solving-quadratics-by-taking-square-roots 2022-10-06T23:01:00.745424633Z Solving quadratics by taking square roots examples Sal solves the equation (x+3)²-4=0 and finds the x-intercepts of f(x)=(x-2)²-9. video https://cdn.kastatic.org/ka_thumbnails_cache/aa5db89d-3db4-43f4-8a80-c766c8298b23_1280_720_base.png Solving quadratics by taking square roots examples Sal solves the equation (x+3)²-4=0 and finds the x-intercepts of f(x)=(x-2)²-9. https://cdn.kastatic.org/ka-youtube-converted/VTlvg4wJ1X0.mp4/VTlvg4wJ1X0.mp4 312 Quadratic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/e/solving_quadratics_by_taking_the_square_root 2021-08-05T05:39:12.794526445Z Quadratics by taking square roots Solve quadratic equations of the form (x+a)²-b=0. These can be solved using square roots. For example, solve (x-5)²-4=0. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/v/determining-mistakes-in-steps-example 2021-06-30T17:32:34Z Quadratics by taking square roots: strategy Sal analyzes a given solution of a quadratic equation, and finds where and what was the error in that process. Sal Khan video https://cdn.kastatic.org/googleusercontent/drMZpLfmtPpYf_DCZKiZK2uHV3oPrRcV8PbR6yzkfSaGaOB15e6NnZ-5A7SoetJiSLLz35fCM5U4srQNpfmLN90 Quadratics by taking square roots: strategy Sal analyzes a given solution of a quadratic equation, and finds where and what was the error in that process. https://cdn.kastatic.org/ka-youtube-converted/jtPvDycHVQw.mp4/jtPvDycHVQw.mp4 105 Quadratic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/e/understanding-the-equation-solving-process 2023-12-12T00:32:03.629852833Z Quadratics by taking square roots: strategy Analyze the process of solving a quadratic equation by taking the square root. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/v/order-of-steps-exercise-example 2021-07-03T04:45:07Z Solving quadratics by taking square roots: with steps Sal discusses the exact order of steps in the process of solving the equation 3(x+6)^2=75. Sal Khan video https://cdn.kastatic.org/googleusercontent/Ika8CfZq3EQADYV4LD74U3B5v4UdpvCaSgDiJcD09qIDbsT1OqtlmxtoXlcwDUoKdyDcaUHVa7NvxYA7Aod5JZdH Solving quadratics by taking square roots: with steps Sal discusses the exact order of steps in the process of solving the equation 3(x+6)^2=75. https://cdn.kastatic.org/ka-youtube-converted/naVFTNWVlQU.mp4/naVFTNWVlQU.mp4 265 Quadratic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/e/quadratics-by-taking-square-roots-with-steps 2026-04-08T00:54:09.631945657Z Quadratics by taking square roots: with steps Give a detailed solution of quadratic equations. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/v/using-the-quadratic-formula 2021-06-30T17:32:40Z The quadratic formula The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations. Sal Khan video https://cdn.kastatic.org/googleusercontent/x7GMr1ACeXuHJxVrjRWD7PnrOmWXP8RdAjYQyJIBuYA1UYmxrOwDqo4u3gWw57OamhGPgBEdToapBY9bOSG2-gbfwA The quadratic formula The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations. https://cdn.kastatic.org/ka-youtube-converted/i7idZfS8t8w.mp4/i7idZfS8t8w.mp4 992 Quadratic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/v/quadratic-formula-2 2021-06-30T17:32:40Z Worked example: quadratic formula (example 2) Sal solves the equation -x^2+8x=1 by first bringing it to standard form and then using the quadratic formula. Sal Khan video https://cdn.kastatic.org/googleusercontent/V_OTYqvz0Vs_SXee7q3w9pxBm_LI-hlUpJHfTG6ntIEprr8GTNbKgoqDtqNWmVDKyd-2H_yHxAtfS-mm2ltubQRX Worked example: quadratic formula (example 2) Sal solves the equation -x^2+8x=1 by first bringing it to standard form and then using the quadratic formula. https://cdn.kastatic.org/ka-youtube-converted/CLrImGKeuEI.mp4/CLrImGKeuEI.mp4 400 Quadratic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/v/applying-the-quadratic-formula 2021-06-30T17:32:39Z Worked example: quadratic formula (negative coefficients) Sal solves -3x^2+10x-3=0 by plugging a=-3, b=10, c=-3 in the quadratic formula. Then he multiplies everything by -1 and solves again. The results are the same! Sal Khan video https://cdn.kastatic.org/googleusercontent/VZTEh4UutBXDxjGxuABZwxG9LaMkHXpBkzp-tS4O29i6ZoaXdlORU-fQYqBE1UXKXT06k7vmCsr7ipfTlEoh7Ko Worked example: quadratic formula (negative coefficients) Sal solves -3x^2+10x-3=0 by plugging a=-3, b=10, c=-3 in the quadratic formula. Then he multiplies everything by -1 and solves again. The results are the same! https://cdn.kastatic.org/ka-youtube-converted/_E3gx_yQhHQ.mp4/_E3gx_yQhHQ.mp4 291 Quadratic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/a/quadratic-formula-explained-article 2021-06-30T17:32:37Z Understanding the quadratic formula Gain more insight into the quadratic formula and how it is used in quadratic equations. article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/e/quadratic_equation 2025-12-28T12:18:45.238308434Z Quadratic formula Solve quadratic equations using the quadratic formula. For example, solve -9x+10x²+8=14. exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/v/quadratic-formula-3 2021-06-30T17:32:40Z Using the quadratic formula: number of solutions Sal determines how many solutions the equation x²+14x+49=0 has by considering its quadratic formula, and more specifically, its discriminant. Sal Khan video https://cdn.kastatic.org/googleusercontent/tME4PRNM9reIhRtam5gf08p-f3rTVvAUySKkYVhiXETYW2OVGb067h40e5z7ZvPDtCie_-_v3GpBKKAH1CckUb-I Using the quadratic formula: number of solutions Sal determines how many solutions the equation x²+14x+49=0 has by considering its quadratic formula, and more specifically, its discriminant. https://cdn.kastatic.org/ka-youtube-converted/XUvKjC21fYU.mp4/XUvKjC21fYU.mp4 299 Quadratic equations https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/a/quadratic-formula-review 2021-06-30T17:32:37Z Quadratic formula review The quadratic formula allows us to solve any quadratic equation that's in the form ax^2 + bx + c = 0. This article reviews how to apply the formula. article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/a/discriminant-review 2023-06-13T22:35:48.054857993Z Discriminant review The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions. article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-formula-a1/e/determine-the-number-of-solutions-of-a-quadratic-equation 2025-12-28T12:18:45.238308434Z Number of solutions of quadratic equations Analyze quadratic equations in order to determine how many different real number solutions they have. Tomer Gal exercise