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

Question

Quizplus · Accepted Answer

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

Solve by Completing the Square y2+5y−5=0y ^ { 2 } + 5 y - 5 = 0y2+5y−5=0

Solve by Completing the Square $y ^ { 2 } + 5 y - 5 = 0$