# How do you solve 8x^2+32x-24 by completing the square?

Mar 20, 2017

$x = - 2 + \sqrt{7} , - 2 - \sqrt{7}$

#### Explanation:

$8 {x}^{2} + 32 x - 24 = 0$

reduce coefficient ${x}^{2}$ to 1 by dividing with $8$
${x}^{2} + 4 x - 3 = 0$

consider coefficient of $x$ and divide by 2 then make a parentesis and square them, then square the number in parentesis and deduct it in the equation.
${\left(x + 2\right)}^{2} - {\left(2\right)}^{2} - 3 = 0$
${\left(x + 2\right)}^{2} - 4 - 3 = 0$
${\left(x + 2\right)}^{2} - 7 = 0$
${\left(x + 2\right)}^{2} = 7$
$\left(x + 2\right) = \pm \sqrt{7}$
$x = - 2 \pm \sqrt{7}$

$x = - 2 + \sqrt{7} , - 2 - \sqrt{7}$