Use the method of completing the square to solve the quadratic equation. 2 x 2 + 6 x $-$ 5 = 0
A) $x = \frac { - 6 + \sqrt { 19 } } { 2 } , x = \frac { 6 + \sqrt { 19 } } { 2 }$
B) $x = \frac { - 3 + \sqrt { 19 } } { 2 } , x = \frac { - 3 - \sqrt { 19 } } { 2 }$
C) $x = \frac { 6 + \sqrt { 19 } } { 2 } , x = \frac { - 6 - \sqrt { 19 } } { 2 }$

Question

Quizplus · Accepted Answer

To complete the square, we want to make the coefficient of the squared term 1. We can do this by dividing the entire equation by 2: 
$$x^2 + 3x - \frac{5}{2} = 0$$
Now we want to find a constant that we can add to both sides so that the left side becomes a perfect square. To do this, we take half of the coefficient of the $x$ term, square it, and add it to both sides:
$$x^2 + 3x + \frac{9}{4} - \frac{5}{2} = \frac{9}{4}$$
Simplifying the left side gives us:
$$\left(x + \frac{3}{2}\right)^2 - \frac{19}{4} = 0$$
Adding $\frac{19}{4}$ to both sides and taking the square root of both sides gives us:
$$x + \frac{3}{2} = \pm \frac{\sqrt{19}}{2}$$
Subtracting $\frac{3}{2}$ from both sides gives us the two solutions:
$$x = \frac{-3 \pm \sqrt{19}}{2}$$
Therefore, the answer is choice B.

Use the Method of Completing the Square to Solve the Quadratic