Solve the quadratic equation by completing the square and applying the square root property.
-$$u ^ { 2 } + 20 u + 101 = 0$$
A) $\{ - 10 \pm i \}$
B) $\{ - 10 + i \}$
C) $\{ 10 + i \}$
D) $\{ \pm i \}$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $u^2 + 20u + 101 = 0$ by completing the square, we first move the constant term to the other side: $u^2 + 20u = -101$. Then, we add $(\frac{20}{2})^2 = 100$ to both sides to complete the square: $u^2 + 20u + 100 = -1$, which simplifies to $(u + 10)^2 = -1$. Taking the square root of both sides gives $u + 10 = \pm \sqrt{-1}$, or $u = -10 \pm i$, where $i$ is the imaginary unit.

Solve the Quadratic Equation by Completing the Square and Applying u2+20u+101=0u ^ { 2 } + 20 u + 101 = 0u2+20u+101=0

Solve the Quadratic Equation by Completing the Square and Applying $u ^ { 2 } + 20 u + 101 = 0$