Solve the equation by completing the square.
-$$x ^ { 2 } - 8 x - 7 = 0$$
A) $\{ 4 - \sqrt { 23 } , 4 + \sqrt { 23 } \}$
B) $\{ 4 - \sqrt { 7 } , 4 + \sqrt { 7 } \}$
C) $\{ - 4 - \sqrt { 23 } , - 4 + \sqrt { 23 } \}$
D) $\{ 8 - \sqrt { 71 } , 8 + \sqrt { 71 } \}$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 - 8x - 7 = 0$ by completing the square, first move the constant term to the other side: $x^2 - 8x = 7$. Then, add $(\frac{-8}{2})^2 = 16$ to both sides to complete the square: $x^2 - 8x + 16 = 23$. This gives $(x - 4)^2 = 23$, so $x - 4 = \pm\sqrt{23}$, leading to the solutions $x = 4 \pm \sqrt{23}$.

Solve the Equation by Completing the Square x2−8x−7=0x ^ { 2 } - 8 x - 7 = 0x2−8x−7=0

Solve the Equation by Completing the Square $x ^ { 2 } - 8 x - 7 = 0$