Completing the Square
Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 8 of 51.
A square is easy to undo. If (x + 2)^2 = 16, then x + 2 is 4 or -4, so x is 2 or -6. Completing the square turns any quadratic equation into that shape, so one square root does the rest.
Take x^2 + 4x - 12 = 0. Move the number across: x^2 + 4x = 12. The left side is one number short of a perfect square, and the missing number is (b/2)^2, which is 4. Add 4 to both sides so the equation stays true: x^2 + 4x + 4 = 16. Now the left is (x + 2)^2, so (x + 2)^2 = 16.
From there, take the square root of both sides with both signs, as in the first paragraph. Keeping both signs matters, because a square hides the sign of what was squared.
Challenge
Solve x^2 + 8x + 7 = 0 by completing the square. The formula and factoring are switched off for this one.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Quadratics & Complex Numbers
2Completing the Square
Perfect Square TrinomialsThe Missing NumberCompleting the SquareIrrational AnswersWhen a Is Not 1Recap: Completing the Square5Complex Arithmetic
Adding and SubtractingMultiplyingThe ConjugateDividingA Pure Imaginary BottomRecap: Complex Arithmetic8Lines Meet Parabolas
Two CrossingsJust TouchingNo MeetingA Circle and a LineRecap: Lines and Parabolas