To solve the quadratic equation \( 5(x - 5)^2 - 33 = -28 \), we can first simplify the equation:
- Start by moving \(-28\) to the left side of the equation:
\[ 5(x - 5)^2 - 33 + 28 = 0 \]
This simplifies to:
\[ 5(x - 5)^2 - 5 = 0 \]
- Now, isolate the quadratic term:
\[ 5(x - 5)^2 = 5 \]
- Divide both sides by \(5\):
\[ (x - 5)^2 = 1 \]
- Take the square root of both sides:
\[ x - 5 = \pm 1 \]
- 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:
\[ \boxed{4} \quad \text{and} \quad \boxed{6} \]
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