Solve the equation by completing the square.
-$$x ^ { 2 } + 3 x - 9 = 0$$
A) $\{ - 3 - 3 \sqrt { 5 } , - 3 + 3 \sqrt { 5 } \}$
B) $\left\{ \frac { - 3 - 3 \sqrt { 5 } } { 2 } \right\}$
C) $\left\{ \frac { 3 + 3 \sqrt { 5 } } { 2 } \right\}$
D) $\left\{ \frac { - 3 - 3 \sqrt { 5 } } { 2 } , \frac { - 3 + 3 \sqrt { 5 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

To complete the square, rewrite the equation as $x^2 + 3x = 9$. Add $(\frac{3}{2})^2 = \frac{9}{4}$ to both sides to get $(x + \frac{3}{2})^2 = \frac{45}{4}$. Solving for $x$, we find $x = \frac{-3 \pm 3\sqrt{5}}{2}$.

Solve the Equation by Completing the Square x2+3x−9=0x ^ { 2 } + 3 x - 9 = 0x2+3x−9=0

Solve the Equation by Completing the Square $x ^ { 2 } + 3 x - 9 = 0$