How do you solve the equation 2/3(x+8)^2-66=0?

2 Answers
Fleur
Jul 18, 2017

x=-8+-3sqrt11

Explanation:

2/3(x+8)^2-66=0

2/3(x+8)^2=66 ->add 66 to both sides

color(blue)(3/2)*2/3(x+8)^2=66*color(blue)(3/2) ->multiply both sides by 3/2

(x+8)^2=99

x+8=+-sqrt99 ->take the square root of both sides

x+8=+-3sqrt11 ->simplify the radical

x=-8+-3sqrt11 ->subtract 8 from both sides

Barney V.
Jul 18, 2017

color(magenta)(x=-8+3sqrt11 or x=-8-3sqrt11

Explanation:

2/3(x+8)^2-66=0

:.2/3(x^2+16x+64)-66=0

:.2/3x^2+32/3x+128/3-66=0

:.2/3x^2+32/3x+128/3-198/3=0

:.2/3x^2+32/3x-70/3=0

multiply both sides by 3

:.2x^2+32x-70=0

:.2(x^2+16x-35)=0

:.x^2+16x-35=0

use quadratic formula

:.x=(-b+-sqrt(b^2-4ac))/(2a)

a=1,b=16,c=-35

:.x=(-16+-sqrt(16^2-4(1)(-35)))/((2)(1))

:.x=(-16+-sqrt(256+140))/2

:.x=(-16+-sqrt(396))/2

x=(-16+-sqrt(11*3*3*2*2))/2

:.x=(-16+-6sqrt(11))/2

:.cancel(-16)^color(magenta)(-8)/cancel2^color(magenta)(1)+-(cancel(-6)^color(magenta)(-3)sqrt(11))/cancel2^color(magenta)(1)

:.-8+-3sqrt11

:.color(magenta)(x=-8+3sqrt11,x=-8-3sqrt11

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