Respuesta :
Given:
The equation is:
[tex](x-3)^2+2(x-3)-8=0[/tex]
To find:
The value of x.
Solution:
We have,
[tex](x-3)^2+2(x-3)-8=0[/tex]
Substitute [tex]x-3=u[/tex].
[tex]u^2+2u-8=0[/tex]
Splitting the middle term, we get
[tex]u^2+4u-2u-8=0[/tex]
[tex]u(u+4)-2(u+4)=0[/tex]
[tex](u-2)(u+4)=0[/tex]
Using zero product property, we get
[tex]u-2=0\text{ and }u+4=0[/tex]
[tex]u=2\text{ and }u=-4[/tex]
Now, substitute [tex]u=x-3[/tex].
[tex]x-3=2\text{ and }x-3=-4[/tex]
[tex]x=2+3\text{ and }x=-4+3[/tex]
[tex]x=5\text{ and }x=-1[/tex]
Therefore, the correct option is b.
The solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.
Quadratic equation
From the question, we are to determine the solution of the given equation
(x - 3)² + 2(x - 3) - 8 = 0
First, we will expand the equation and clear the brackets
[tex](x - 3)^{2} + 2(x - 3) - 8 = 0[/tex]
[tex](x - 3)(x - 3) + 2(x - 3) - 8 = 0[/tex]
[tex]x^{2} -6x + 9 +2x - 6 - 8 = 0[/tex]
Simplifying
[tex]x^{2} -4x - 5 = 0[/tex]
Factorizing, we get
[tex]x^{2} -5x +x- 5 = 0[/tex]
[tex]x(x-5)+1(x- 5) = 0[/tex]
[tex](x+1)(x-5)= 0[/tex]
Then,
x + 1 = 0 or x - 5 = 0
x = -1 or x = 5
Hence, the solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.
Learn more on solving Quadratic equations here: https://brainly.com/question/8649555
