How do you solve x + 9 = 2(x - 1)^2?

1 Answer
Apr 15, 2018

x_1=7/2
x_2=-1

Explanation:

x+9=2(x^2-2x+1)

x+9=2x^2-4x+2

-2x^2+x+4x+9-2=0

-2x^2+5x+7=0 //*(-1)

2x^2-5x-7=0

Now use the formula x_(1//2)=(-b+-sqrt(b^2-4ac))/(2a)
a=2
b=-5
c=-7

x_(1//2)=(5+-sqrt((25-4*2(-7))))/(2*2)

x_(1//2)=(5+-sqrt((25+56)))/4

x_(1//2)=(5+-sqrt(81))/4

x_(1//2)=(5+-9)/4

x_1=(5+9)/4=14/4=7/2

x_2=(5-9)/4=(-4)/4=-1