# How do you solve using the completing the square method 7x²+9x+1=0 ?

Mar 3, 2018

color(green)(x = -1.5429, -2.9571

#### Explanation:

$7 {x}^{2} + 9 x + 1 = 0$

$\cancel{7} \left({x}^{2} + \left(\frac{9}{7}\right) x + \left(\frac{1}{7}\right)\right) = 0$

(x^2 + (2 * (9/14) x) = -(1/7)

Add ${\left(\frac{9}{14}\right)}^{2}$ to both sides.

${x}^{2} + \left(2 \cdot \left(\frac{9}{14}\right) x\right) + {\left(\frac{9}{14}\right)}^{2} = - \frac{1}{7} + \frac{9}{14} = \frac{1}{2}$

(x+ 9/14))^2 = (sqrt (1/2))^2

$x + \left(\frac{9}{4}\right) = \pm \sqrt{\frac{1}{2}}$

$x = + \sqrt{\frac{1}{2}} - \left(\frac{9}{4}\right) , - \sqrt{\frac{1}{2}} - \left(\frac{9}{4}\right)$

color(green)(x = -1.5429, -2.9571