# How do you solve using the completing the square method 3x^2 + 15x = 9?

##### 1 Answer

$x = \frac{- 5 + \sqrt{37}}{2}$ and $x = \frac{- 5 - \sqrt{37}}{2}$

#### Explanation:

From the given

$3 {x}^{2} + 15 x = 9$

divide both sides of the equation by 3 first, to make the coefficient of ${x}^{2}$ equal to 1

$\frac{3 {x}^{2}}{3} + \frac{15 x}{3} = \frac{9}{3}$

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

Divide now the numerical coefficient of x by 2 then square the result. Let the result be added to both sides of the equation

${x}^{2} + 5 x + \frac{25}{4} = 3 + \frac{25}{4}$

We now have the Perfect Square Trinomial
${\left(x + \frac{5}{2}\right)}^{2} = \frac{37}{4}$
Extract square root of both sides

$\sqrt{{\left(x + \frac{5}{2}\right)}^{2}} = \sqrt{\frac{37}{4}}$

$x + \frac{5}{2} = \pm \frac{1}{2} \sqrt{37}$

$x = - \frac{5}{2} \pm \frac{1}{2} \sqrt{37}$

we have 2 values

$x = - \frac{5}{2} + \frac{1}{2} \sqrt{37}$ and $x = - \frac{5}{2} - \frac{1}{2} \sqrt{37}$

God bless....I hope the explanation is useful.