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

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Answer 1 · 2018-05-28T15:27:45

$x = - \frac{23}{4} \pm \sqrt{\frac{249}{4}}$ $x=-23/4+-sqrt(249/4)$

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

$3 x + 2 (x + 5) (x + 5) = 15$ $3x+2(x+5)(x+5)=15$

FOIL

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

Distribute the 2

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

Combine like terms:

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

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

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x=(-b+-sqrt(b^2 - 4ac))/(2a)$

a=2
b=23
c=35

$x = - \frac{23}{4} \pm \sqrt{\frac{249}{4}}$ $x=-23/4+-sqrt(249/4)$

What is x if 3x+2(x+5)2=153x+2(x+5)^2=15?