# How do you solve the quadratic equation by completing the square: x^2 - 3x = 4?

##### 1 Answer
Jul 20, 2015

I found:
${x}_{1} = - 1$
${x}_{2} = 4$

#### Explanation:

You can try adding and subtracting $\frac{9}{4}$ on the left side:
${x}^{2} - 3 x \textcolor{red}{+ \frac{9}{4} - \frac{9}{4}} = 4$
rearranging:
${x}^{2} - 3 x + \frac{9}{4} = 4 + \frac{9}{4}$
${\left(x - \frac{3}{2}\right)}^{2} = \frac{16 + 9}{4}$
square root both sides:
$x - \frac{3}{2} = \pm \sqrt{\frac{25}{4}} = \pm \frac{5}{2}$
So, you get two solutions:
${x}_{1} = \frac{5}{2} + \frac{3}{2} = 4$
${x}_{2} = - \frac{5}{2} + \frac{3}{2} = - 1$