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 Completar el cuadrado https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/e/completing_the_square_in_quadratic_expressions 2025-12-28T12:18:45.238308434Z Completing the square (intro) Practice the method of completing the square with quadratic expressions. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/v/ex1-completing-the-square 2021-06-30T17:32:40Z Worked example: Completing the square (intro) Sal completes x²-44x into a perfect square. Sal Khan video https://cdn.kastatic.org/googleusercontent/02Zup7B5Tm4ksL9AcJ9c6zpWztcA11VJoDoCrYYThds7Sa4XD03-k4b6M-tlGwkLO1GiBVkWrFph89YfEAAY0-U Worked example: Completing the square (intro) Sal completes x²-44x into a perfect square. https://cdn.kastatic.org/ka-youtube-converted/VvuuRpJbbHE.mp4/VvuuRpJbbHE.mp4 202 Completar el cuadrado https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/v/rewriting-quadratics-as-perfect-squares 2022-10-06T23:01:00.745424633Z Worked example: Rewriting expressions by completing the square Sal rewrites x²+16x+9 as (x+8)²-55 by completing the square. video https://cdn.kastatic.org/ka_thumbnails_cache/fb1361a3-e313-443f-a548-d7862af784e0_1280_720_base.png Worked example: Rewriting expressions by completing the square Sal rewrites x²+16x+9 as (x+8)²-55 by completing the square. https://cdn.kastatic.org/ka-youtube-converted/sh-MP-dVhD4.mp4/sh-MP-dVhD4.mp4 182 Completar el cuadrado 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:more-on-completing-square/v/solve-completing-square-integer-solutions 2022-09-10T01:04:29.754011735Z Solve by completing the square: Integer solutions We can use the strategy of completing the square to solve quadratic equations. If the solutions are integers, we can solve by factoring as well. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/d0ed036b-ffee-4fdf-898d-dfc1967f993a_1280_720_base.png Solve by completing the square: Integer solutions We can use the strategy of completing the square to solve quadratic equations. If the solutions are integers, we can solve by factoring as well. https://cdn.kastatic.org/ka-youtube-converted/eU41vG9z35M.mp4/eU41vG9z35M.mp4 389 Completar el cuadrado https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/v/solve-completing-square-non-integer-solutions 2022-09-10T01:04:29.754011735Z Solve by completing the square: Non-integer solutions We can use the strategy of completing the square to solve quadratic equations even when the solutions aren't integers. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/62b67f95-76b4-4289-8785-edb115354075_1280_720_base.png Solve by completing the square: Non-integer solutions We can use the strategy of completing the square to solve quadratic equations even when the solutions aren't integers. https://cdn.kastatic.org/ka-youtube-converted/Ldp9_K3L4Q8.mp4/Ldp9_K3L4Q8.mp4 242 Completar el cuadrado https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/e/solve-completing-square 2025-09-02T23:00:39.251995325Z Solve equations by completing the square Practice solving quadratic equations by completing the square. Jeff Dodds exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/v/completing-the-square-to-solve-quadratic-equations 2021-06-30T17:32:39Z Worked example: completing the square (leading coefficient ≠ 1) Sal solves the equation 4x^2+40x-300=0 by completing the square. Sal Khan video https://cdn.kastatic.org/googleusercontent/Xfk8YyNRDZjqMMWQhG8mMFqvMosMnuSX5E7DZkggk7LKu1ZGRBDLZfiZhpSVpxRs51hLPLREZsIcwiWzWXuVie8 Worked example: completing the square (leading coefficient ≠ 1) Sal solves the equation 4x^2+40x-300=0 by completing the square. https://cdn.kastatic.org/ka-youtube-converted/TV5kDqiJ1Os.mp4/TV5kDqiJ1Os.mp4 344 Completar el cuadrado https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/a/solving-quadratic-equations-by-completing-the-square 2023-11-10T19:13:09.242227712Z Solving quadratics by completing the square For example, solve x²+6x=-2 by manipulating it into (x+3)²=7 and then taking the square root. article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/e/completing_the_square_2 2025-12-05T14:00:44.642338931Z Completing the square Solve quadratic equations of the form ax^2+bx+c by completing the square. 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 Completar el cuadrado 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:more-on-completing-square/v/proof-of-quadratic-formula 2021-06-30T17:32:38Z Proof of the quadratic formula Sal proves the quadratic formula using the method of completing the square. Sal Khan video https://cdn.kastatic.org/googleusercontent/CTdKwqBQ1YrTcbA80JUfi-LzbCaaFguVSd_-xctPRcoyDZC5aKSTra46tvNl9t-SS1PUJy_3D3bkQk8Z0X7YvTVKww Proof of the quadratic formula Sal proves the quadratic formula using the method of completing the square. https://cdn.kastatic.org/ka-youtube-converted/r3SEkdtpobo.mp4/r3SEkdtpobo.mp4 464 Completar el cuadrado https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/a/quadratic-formula-proof-review 2021-06-30T17:32:37Z Quadratic formula proof review A text-based proof (not video) of the quadratic formula article