How do you solve \frac { 3} { 2} ( x - 10) ^ { 2} = \frac { 1} { 2}32(x10)2=12?

1 Answer
Jul 22, 2017

x={(30+sqrt3)/3 , (30-sqrt3)/3}x={30+33,3033}

Explanation:

3/2(x-10)^2=1/232(x10)2=12
Multiply both by 2
3(x-10)^2=13(x10)2=1
3(x^2-20+100)=13(x220+100)=1
3x^2-60+300=13x260+300=1
3x^2-60+299=03x260+299=0

We know that if ax^2+bx+c=0ax2+bx+c=0 then x=(-b+-sqrt(b^2-4ac))/(2a)x=b±b24ac2a

So x=(-(-60)+-sqrt(60^2-4*3*299))/(2*3)x=(60)±6024329923
x=(60+-sqrt(3600-3588))/6x=60±360035886
x=(60+-sqrt(12))/6x=60±126
x=(60+-2sqrt3)/6x=60±236
x=(30+-sqrt3)/3x=30±33

So, x=(30+sqrt3)/3x=30+33 or x=(30-sqrt3)/3x=3033