Solve the equation by completing the square.
-$$x ^ { 2 } + x + 6 = 0$$
A) $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$
B) $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$
C) $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } \mathrm { i }$
D) $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } i$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + x + 6 = 0$ by completing the square, first move the constant term to the other side: $x^2 + x = -6$. Then, add $\left(\frac{1}{2}\right)^2 = \frac{1}{4}$ to both sides to complete the square: $x^2 + x + \frac{1}{4} = -6 + \frac{1}{4}$, which simplifies to $(x + \frac{1}{2})^2 = -\frac{23}{4}$. Taking the square root of both sides gives $x + \frac{1}{2} = \pm \sqrt{-\frac{23}{4}}$, which simplifies to $x = -\frac{1}{2} \pm \frac{\sqrt{23}}{2}i$, indicating the solutions are complex.

Solve the Equation by Completing the Square x2+x+6=0x ^ { 2 } + x + 6 = 0x2+x+6=0

Solve the Equation by Completing the Square $x ^ { 2 } + x + 6 = 0$