Algebra 1, Please Help! Square Roots and Completing the Square

Question

Solve the equation using the Complete The Square Method, show all your work/steps.

x² + 12x = 13

Answer 1

Hi Candi,

x² + 12x = 13 --- Given equation

x² + 6x + 6x = 13 --- 12x = 2 (6x) = 6x + 6x

x² + 6x + 6x + 6² = 13 + 6² --- Add 6² on both sides to complete the square

x² + 6x + 6x + 6² = 7² --- 13 + 6² = 13 + 36 = 49 = 7²

x(x + 6) + 6(x + 6) = 7²

(x + 6) (x + 6) = 7²

(x + 6)² = 7²

x + 6 = ± 7

x + 6 = 7 or x + 6 = - 7

-6 -6 -6 - 6 --- Subtract 6 on both sides

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x = 1 x = - 13

So , x = 1 , -13 are the solutions for the given equation.

Hope this helps!

Answer 2