What is x if 3x+2(x+5)^2=15?

May 28, 2018

$x = - \frac{23}{4} \pm \sqrt{\frac{249}{4}}$

Explanation:

$3 x + 2 {\left(x + 5\right)}^{2} = 15$

$3 x + 2 \left(x + 5\right) \left(x + 5\right) = 15$

FOIL

$3 x + 2 \left({x}^{2} + 10 x + 25\right) = 15$

Distribute the 2

$3 x + 2 {x}^{2} + 20 x + 50 = 15$

Combine like terms:

$2 {x}^{2} + 23 x + 35 = 0$

you will need to use the quadratic formula to solve the roots:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

a=2
b=23
c=35

$x = - \frac{23}{4} \pm \sqrt{\frac{249}{4}}$