Question

Solve the following quadratic equation for all values of xx in simplest form.
5, left parenthesis, x, minus, 5, right parenthesis, squared, minus, 33, equals, minus, 28
5(x−5)
2
−33=
−28

Answer 1

To solve the quadratic equation \( 5(x - 5)^2 - 33 = -28 \), we can first simplify the equation:

1. Start by moving \(-28\) to the left side of the equation:

\[
5(x - 5)^2 - 33 + 28 = 0
\]

This simplifies to:

\[
5(x - 5)^2 - 5 = 0
\]

2. Now, isolate the quadratic term:

\[
5(x - 5)^2 = 5
\]

3. Divide both sides by \(5\):

\[
(x - 5)^2 = 1
\]

4. Take the square root of both sides:

\[
x - 5 = \pm 1
\]

5. This gives us two cases to solve for \(x\):

**Case 1:**

\[
x - 5 = 1
\]

Add \(5\) to both sides:

\[
x = 6
\]

**Case 2:**

\[
x - 5 = -1
\]

Add \(5\) to both sides:

\[
x = 4
\]

Thus, the solutions to the equation are:

\[
\boxed{4} \quad \text{and} \quad \boxed{6}
\]