To solve the factored quadratic equation \((x - 5)(x + 3) = 0\), you can use the zero product property which states that if a product of two factors equals zero, at least one of the factors must be zero.
Setting each factor to zero gives:
- \(x - 5 = 0\)
- \(x + 3 = 0\)
Solving these equations:
-
From \(x - 5 = 0\): \[ x = 5 \]
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From \(x + 3 = 0\): \[ x = -3 \]
Now, we have the solutions: \(x = 5\) and \(x = -3\).
The smaller solution is \(x = -3\), and the larger solution is \(x = 5\).
So, the final answers are:
- The smaller solution is \(x = -3\).
- The larger solution is \(x = 5\).