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

Question

Quizplus · Accepted Answer

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

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

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