Question

Solve x^2 + 6x = 7 by completing the square. Which is the solution set of the equation?
O {-7, 1}
O-3√10, -3 + √10}
O (3√10, 3+ √10}
O {1,7}

Answer 1

Answer: Choice A.   {-7, 1}

Work Shown:

$x^2 + 6x = 7\\\\x^2 + 6x+9 = 7+9\\\\x^2 + 6x+9 = 16\\\\(x+3)^2 = 16\\\\x+3 = \pm\sqrt{16}\\\\x+3 = 4 \text{ or } x+3 = -4\\\\x = 4-3 \text{ or } x = -4-3\\\\x = 1 \text{ or } x = -7$

I added 9 to both sides (second step) by first taking half of the x coefficient 6, then squaring the result

6/2 = 3 which squares to 9.

This step is done to complete the square.

Visual verification is shown below. The x intercepts are -7 and 1. They are located at (-7,0) and (1,0) respectively. I graphed x^2+6x-7 by getting everything to one side in the original equation.