Solve the quadratic equation by completing the square.
-$x ^ { 2 } - 8 x + 11 = 0$
A) $4 \pm \sqrt { 5 }$
B) $- 8 \pm 2 \sqrt { 5 }$
C) $- 4 \pm \sqrt { 5 }$
D) $8 \pm \sqrt { 5 }$

Question

Solve the quadratic equation by completing the square.
-$x ^ { 2 } - 8 x + 11 = 0$
A) $4 \pm \sqrt { 5 }$
B)  $- 8 \pm 2 \sqrt { 5 }$
C) $- 4 \pm \sqrt { 5 }$
D) $8 \pm \sqrt { 5 }$

Quizplus · Accepted Answer

To solve the quadratic equation $x^2 - 8x + 11 = 0$ by completing the square, we first move the constant term to the other side: $x^2 - 8x = -11$. Then, we add $(\frac{-8}{2})^2 = 16$ to both sides to complete the square: $x^2 - 8x + 16 = 5$. This gives us $(x - 4)^2 = 5$, so $x - 4 = \pm \sqrt{5}$. Solving for $x$ gives $x = 4 \pm \sqrt{5}$.

Solve the Quadratic Equation by Completing the Square x2−8x+11=0x ^ { 2 } - 8 x + 11 = 0x2−8x+11=0

Solve the Quadratic Equation by Completing the Square $x ^ { 2 } - 8 x + 11 = 0$