Question

solve the equation in quadratic form, ((2x - 3)^2 - 2(2x - 3) - 15 = 0).

select one:
a. (x = 5, 3)
b. (x = -3, 5)
c. (x = -4, 0)
d. (x = 0, 4)

Explanation:

Step1: Substitute to simplify equation

Let $u = 2x - 3$. The equation becomes:
$$u^2 - 2u - 15 = 0$$

Step2: Factor the quadratic equation

Find two factors of -15 that sum to -2:
$$(u - 5)(u + 3) = 0$$

Step3: Solve for $u$

Set each factor equal to 0:
$u - 5 = 0 \implies u = 5$
$u + 3 = 0 \implies u = -3$

Step4: Substitute back to solve for $x$

For $u=5$:
$2x - 3 = 5 \implies 2x = 8 \implies x = 4$
For $u=-3$:
$2x - 3 = -3 \implies 2x = 0 \implies x = 0$

Answer:

D. $x = 0, 4$