Solve the equation by completing the square.
-$$\mathrm { p } ^ { 2 } + 3 \mathrm { p } - 9 = 0$$
A) $- \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 5 } } { 2 }$
B) $- 3 \pm 3 \sqrt { 5 }$
C) $\frac { 3 } { 2 } \pm \frac { 3 \sqrt { 5 } } { 2 }$
D) $- \frac { 3 } { 2 } + \frac { 3 \sqrt { 5 } } { 2 }$

Question

Quizplus · Accepted Answer

To solve the equation $p^2 + 3p - 9 = 0$ by completing the square, first move the constant term to the other side: $p^2 + 3p = 9$. Then, add $\left(\frac{3}{2}\right)^2 = \frac{9}{4}$ to both sides to complete the square: $p^2 + 3p + \frac{9}{4} = 9 + \frac{9}{4} = \frac{36}{4} + \frac{9}{4} = \frac{45}{4}$. This gives $\left(p + \frac{3}{2}\right)^2 = \frac{45}{4}$, so $p + \frac{3}{2} = \pm \sqrt{\frac{45}{4}}$, leading to $p = -\frac{3}{2} \pm \frac{\sqrt{45}}{2}$. Simplifying $\sqrt{45}$ to $3\sqrt{5}$ gives $p = -\frac{3}{2} \pm \frac{3\sqrt{5}}{2}$.

Solve the Equation by Completing the Square p2+3p−9=0\mathrm { p } ^ { 2 } + 3 \mathrm { p } - 9 = 0p2+3p−9=0

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