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

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Answer 1 · 2018-04-15T19:15:23

#x_1=7/2#
#x_2=-1#

#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#