Question

What are the solutions of the equation (x-3)^2 + 2(x-3) -8 = 0

Answer 1

expand and simplify
(x-3) (x-3) +2(x-3) -8=0
(x-3+2)(x-3)-8=0
(x-1)(x-3)-8=0
x^2 -4x +3-8=0
x^2 - 4x -5=0
x^2 -5x +x-5=0
x(x-5)+x-5=0
(x+1)(x-5)=0
x= - 1, 5

Answer 2

Hello,
(x-3)²+2(x-3)-8=0
x²-6x+9+2x-6-8=0
x²-4x-5=0
∆=b²-4ac=(4)²-4(-5)(1)=16+20=36
x₁,₂=-b±√∆/2a=4±6/2
x₁=4-6/2=-2/2=-1
x₂=4+6/2=10/2=5

Therefore the solutions are
x=-1 and x=5

See you soon :-)