Solve by completing the square.
-$$x ^ { 2 } + 8 x = 7$$
A) $4 + \sqrt { 23 }$
B) $- 1 \pm \sqrt { 23 }$
C) $- 4 \pm \sqrt { 23 }$
D) $- 4 \pm 2 \sqrt { 23 }$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + 8x = 7$ by completing the square, first move the constant term to the other side to get $x^2 + 8x - 7 = 0$. Then, add and subtract $(\frac{8}{2})^2 = 16$ inside the equation to complete the square, leading to $x^2 + 8x + 16 = 7 + 16$, which simplifies to $(x + 4)^2 = 23$. Taking the square root of both sides gives $x + 4 = \pm \sqrt{23}$, so $x = -4 \pm \sqrt{23}$.

Solve by Completing the Square x2+8x=7x ^ { 2 } + 8 x = 7x2+8x=7

Solve by Completing the Square $x ^ { 2 } + 8 x = 7$