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

Question

Quizplus · Accepted Answer

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

Solve by Completing the Square to Obtain Exact Solutions x2+5x−5=0x ^ { 2 } + 5 x - 5 = 0x2+5x−5=0

Solve by Completing the Square to Obtain Exact Solutions $x ^ { 2 } + 5 x - 5 = 0$