Solve the equation by completing the square.
-$$z ^ { 2 } + 10 z + 11 = 0$$
A) $5 \pm \sqrt { 11 }$
B) $- 10 + \sqrt { 11 }$
C) $- 5 \pm \sqrt { 14 }$
D) $5 + \sqrt { 14 }$

Question

Quizplus · Accepted Answer

To solve the equation $z^2 + 10z + 11 = 0$ by completing the square, we first move the constant term to the other side: $z^2 + 10z = -11$. Then, we add $\left(\frac{10}{2}\right)^2 = 25$ to both sides to complete the square: $z^2 + 10z + 25 = 14$. This gives us $(z + 5)^2 = 14$, so $z + 5 = \pm \sqrt{14}$, leading to $z = -5 \pm \sqrt{14}$.

Solve the Equation by Completing the Square z2+10z+11=0z ^ { 2 } + 10 z + 11 = 0z2+10z+11=0

Solve the Equation by Completing the Square $z ^ { 2 } + 10 z + 11 = 0$