Solve the equation by completing the square.
-$$x ^ { 2 } + 8 x = 7$$
A) $\{ - 4 - \sqrt { 11.5 } , - 4 + \sqrt { 11.5 } \}$
B) $\{ 4 + \sqrt { 11.5 } \}$
C) $\{ - 1 - \sqrt { 11.5 } , - 1 + \sqrt { 11.5 } \}$
D) $\{ - 4 - 1 \sqrt { 11.5 } , - 4 + 1 \sqrt { 11.5 } \}$

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: $x^2 + 8x - 7 = 0$. Then, add $(\frac{8}{2})^2 = 16$ to both sides to complete the square: $x^2 + 8x + 16 = 7 + 16$, which simplifies to $x^2 + 8x + 16 = 23$. This can be written as $(x + 4)^2 = 23$. Taking the square root of both sides gives $x + 4 = \pm \sqrt{23}$, so $x = -4 \pm \sqrt{23}$. Since $\sqrt{23}$ is approximately $\sqrt{11.5}$, the correct answer is $\{ - 4 - \sqrt { 11.5 } , - 4 + \sqrt { 11.5 } \}$.

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

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