Question

What are the solutions of the equation (x – 3)^2 + 2(x – 3) – 8 = 0? Use u substitution to solve.

x = –5 and x = 1
x = –1 and x = 5
x = –1 and x = –7
x = 1 and x = 7

Answer 1

To solve the equation (x - 3)^2 + 2(x - 3) - 8 = 0 using u substitution, let u = x - 3. Then, solve the resulting quadratic equation for u and substitute the values back into x to find the solutions.

Step-by-step explanation:

To solve the equation (x - 3)^2 + 2(x - 3) - 8 = 0 using u substitution, we can let u = x - 3. This means that x = u + 3. Substituting u + 3 into the equation, we get u^2 + 2u - 8 = 0. Now we can solve this quadratic equation for u.

Factoring the quadratic equation, we have (u - 2)(u + 4) = 0. Setting each factor equal to zero, we get u - 2 = 0 and u + 4 = 0. Solving for u, we find u = 2 and u = -4.

Since u = x - 3, we can substitute these values back into u to find x. Therefore, x = 2 + 3 = 5 and x = -4 + 3 = -1. So the solutions to the equation are x = 5 and x = -1.

Answer 2

The solution is x=-1 and x=5. Why? Well like the question states you just have to substitute each number for x.

((-1)-3)^2+2((-1)-3)-8=0
16+(-8)-8=0
0=0

((5)-3)^2+2((-1)-3)-8=0
4+4-8=0
0=0

Each one is true. Hope this helped! :)