How do you solve x^2 + 3x - 5 = 0 by completing the square?

Apr 6, 2017

$x = - \frac{3}{2} \pm \frac{\sqrt{29}}{4}$

Explanation:

Add $5$ on both sides:

${x}^{2} + 3 x = 5$

Now add ${\left(\frac{b}{2} a\right)}^{2}$ on both sides where $a = 1$ and $b = 3$

${x}^{2} + 3 x + \frac{9}{4} = 5 + \frac{9}{4}$

Rewrite:

${\left(x + \frac{3}{2}\right)}^{2} = \frac{29}{4}$

Square root both sides. Don't forget that it's $\pm$ the square root:

$x + \frac{3}{2} = \pm \sqrt{\frac{29}{4}}$

Subtract $\frac{3}{2}$ on both sides:

$x = - \frac{3}{2} \pm \sqrt{\frac{29}{4}}$