https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/v/solving-quadratic-equations-by-completing-the-square 2021-06-30T17:32:40Z Completing the square Some quadratic expressions can be factored as perfect squares. For example, x²+6x+9=(x+3)². However, even if an expression isn't a perfect square, we can turn it into one by adding a constant number. For example, x²+6x+5 isn't a perfect square, but if we add 4 we get (x+3)². This, in essence, is the method of *completing the square* Sal Khan video https://cdn.kastatic.org/googleusercontent/21D9W6Ar02QOFUD04nwNqQWkMGs_P0mXTmgQ6OxvZu6ArMLD__sLMOQVPkjmMPeDYXPDmK9lFwncADaVJkrg0XNc Completing the square Some quadratic expressions can be factored as perfect squares. For example, x²+6x+9=(x+3)². However, even if an expression isn't a perfect square, we can turn it into one by adding a constant number. For example, x²+6x+5 isn't a perfect square, but if we add 4 we get (x+3)². This, in essence, is the method of *completing the square* https://cdn.kastatic.org/ka-youtube-converted/bNQY0z76M5A.mp4/bNQY0z76M5A.mp4 846 Solving Quadratics by Completing the square https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/v/solving-quadratics-by-completing-the-square 2021-06-30T17:32:34Z Worked example: Rewriting & solving equations by completing the square Sal solves x²-2x-8=0 by rewriting the equation as (x-1)²-9=0 (which is done by completing the square!). video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Worked example: Rewriting & solving equations by completing the square Sal solves x²-2x-8=0 by rewriting the equation as (x-1)²-9=0 (which is done by completing the square!). https://cdn.kastatic.org/ka-youtube-converted/KouDAzYl_bc.mp4/KouDAzYl_bc.mp4 379 Solving Quadratics by Completing the square https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/e/completing_the_square_1 2026-01-08T04:41:12.004642433Z Completing the square (intermediate) Solve quadratic equations of the form x^2+bx+c by completing the square. 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 Solving Quadratics by Completing the square 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:more-on-completing-square/v/ex2-completing-the-square 2021-06-30T17:32:40Z Solving quadratics by completing the square: no solution Sal solves the equation 4x^2+40x+280=0 by completing the square, only to find there's no solution for this equation. Sal Khan video https://cdn.kastatic.org/googleusercontent/bajJeqKcAWCMuD7dt1tG2eNLYffHWt03K1bQToZASG3CjttRps3BsK780FwDDGgwJfzF2SN9j6B1yTIQQ6gSa_Lf Solving quadratics by completing the square: no solution Sal solves the equation 4x^2+40x+280=0 by completing the square, only to find there's no solution for this equation. https://cdn.kastatic.org/ka-youtube-converted/6agzj3A9IgA.mp4/6agzj3A9IgA.mp4 324 Solving Quadratics by Completing the square https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/a/completing-the-square-review 2021-06-30T17:32:35Z Completing the square review Completing the square is a technique for factoring quadratics. This article reviews the technique with examples and even lets you practice the technique yourself. article 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 Solving Quadratics by Completing the square https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/a/solving-simple-quadratics-review 2021-06-30T17:32:37Z Solving simple quadratics review Simple quadratic equations like x^2=4 can be solved by taking the square root. This article reviews several examples and gives you a chance to practice on your own. article 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