Use the method of completing the square to solve the quadratic equation. x 2 + 5 x $-$ 3 = 0
A) $x = \frac { - 5 + \sqrt { 37 } } { 2 } , x = \frac { - 5 - \sqrt { 37 } } { 2 }$
B) $x = \frac { - 5 + \sqrt { 37 } } { 2 } , x = \frac { 5 + \sqrt { 37 } } { 2 }$
C) $x = \frac { 5 + \sqrt { 37 } } { 2 } , x = \frac { - 5 - \sqrt { 37 } } { 2 }$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + 5x - 3 = 0$ by completing the square, first move the constant term to the other side: $x^2 + 5x = 3$. Then, add $(\frac{5}{2})^2 = \frac{25}{4}$ to both sides to complete the square: $x^2 + 5x + \frac{25}{4} = 3 + \frac{25}{4}$, which simplifies to $(x + \frac{5}{2})^2 = \frac{37}{4}$. Taking the square root of both sides gives $x + \frac{5}{2} = \pm \sqrt{\frac{37}{4}}$, leading to $x = -\frac{5}{2} \pm \frac{\sqrt{37}}{2}$, or $x = \frac{-5 \pm \sqrt{37}}{2}$.

Use the Method of Completing the Square to Solve the Quadratic