Question

Solve the following quadratic equation for all values of xx in simplest form.
4, left parenthesis, x, minus, 4, right parenthesis, squared, minus, 33, equals, minus, 5
4(x−4)
2
−33=
−5

Answer 1

Solve 4(x − 4)^2 − 33 = −5.

Step 1: Add 33 to both sides:
4(x − 4)^2 = 28

Step 2: Divide by 4:
(x − 4)^2 = 7

Step 3: Take square roots:
x − 4 = ±√7

Step 4: Solve for x:
x = 4 ± √7

So the solutions are x = 4 + √7 and x = 4 − √7.