Solve the equation by completing the square.
-$$x ^ { 2 } + 5 x - 5 = 0$$
A) $\left\{ \frac { - 5 - 3 \sqrt { 5 } } { 2 } , \frac { - 5 + 3 \sqrt { 5 } } { 2 } \right\}$
B) $\left\{ \frac { 5 + 3 \sqrt { 5 } } { 2 } \right\}$
C) $\left\{ \frac { - 5 - 3 \sqrt { 5 } } { 2 } \right\}$
D) $\{ - 5 - 3 \sqrt { 5 } , - 5 + 3 \sqrt { 5 } \}$

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, add $\left(\frac{5}{2}\right)^2 = \frac{25}{4}$ to both sides to complete the square: $x^2 + 5x + \frac{25}{4} = 5 + \frac{25}{4} = \frac{45}{4}$. This gives $\left(x + \frac{5}{2}\right)^2 = \frac{45}{4}$. Taking the square root of both sides gives $x + \frac{5}{2} = \pm \sqrt{\frac{45}{4}} = \pm \frac{3\sqrt{5}}{2}$. Solving for $x$ yields $x = -\frac{5}{2} \pm \frac{3\sqrt{5}}{2}$, which simplifies to the solutions $\frac{-5 \pm 3\sqrt{5}}{2}$.

Solve the Equation by Completing the Square x2+5x−5=0x ^ { 2 } + 5 x - 5 = 0x2+5x−5=0

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