Question

solve the equation in quadratic form:
$(2x - 3)^2 - 2(2x - 3) - 35 = 0$

select one:
a. $x = -1, 5$
b. $x = -1, -5$
c. $x = -5, -7$
d. $x = -5, 7$

Explanation:

Step1: Substitute $u=2x-3$

Let $u = 2x - 3$, the equation becomes:
$$u^2 - 2u - 35 = 0$$

Step2: Factor the quadratic equation

Find two numbers that multiply to $-35$ and add to $-2$: $-7$ and $5$.
$$(u - 7)(u + 5) = 0$$

Step3: Solve for $u$

Set each factor equal to 0:
$u - 7 = 0 \implies u = 7$
$u + 5 = 0 \implies u = -5$

Step4: Substitute back $u=2x-3$

For $u=7$:
$$2x - 3 = 7$$
$$2x = 10$$
$$x = 5$$
For $u=-5$:
$$2x - 3 = -5$$
$$2x = -2$$
$$x = -1$$

Answer:

A. $x = -1, 5$