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

Question

Quizplus · Accepted Answer

To solve the equation $p^2 + 5p - 5 = 0$ by completing the square, first move the constant term to the other side: $p^2 + 5p = 5$. Then, add $\left(\frac{5}{2}\right)^2 = \frac{25}{4}$ to both sides to complete the square: $p^2 + 5p + \frac{25}{4} = 5 + \frac{25}{4}$, which simplifies to $\left(p + \frac{5}{2}\right)^2 = \frac{45}{4}$. Taking the square root of both sides gives $p + \frac{5}{2} = \pm \sqrt{\frac{45}{4}}$, which simplifies to $p = -\frac{5}{2} \pm \frac{3\sqrt{5}}{2}$.

Solve the Equation by Completing the Square p2+5p−5=0\mathrm { p } ^ { 2 } + 5 \mathrm { p } - 5 = 0p2+5p−5=0

Solve the Equation by Completing the Square $\mathrm { p } ^ { 2 } + 5 \mathrm { p } - 5 = 0$