Use the method of completing the square to solve the quadratic equation. 3 x 2 + 5 x $-$ 1 = 0

Question

Quizplus · Accepted Answer

To solve the quadratic equation $3x^2 + 5x - 1 = 0$ by completing the square, first divide the entire equation by 3 to get $x^2 + \frac{5}{3}x - \frac{1}{3} = 0$. Then, move the constant term to the other side: $x^2 + \frac{5}{3}x = \frac{1}{3}$. To complete the square, add $\left(\frac{5}{6}\right)^2 = \frac{25}{36}$ to both sides, resulting in $x^2 + \frac{5}{3}x + \frac{25}{36} = \frac{1}{3} + \frac{25}{36}$. This simplifies to $\left(x + \frac{5}{6}\right)^2 = \frac{37}{36}$. Taking the square root of both sides gives $x + \frac{5}{6} = \pm \sqrt{\frac{37}{36}}$, which simplifies to $x = -\frac{5}{6} \pm \frac{\sqrt{37}}{6}$, matching choice B.

Use the Method of Completing the Square to Solve the Quadratic