Question

solve for x .
(2x - 16)(x² - 49) = 0
(if there is more than one solution, separate them with commas.)
x =

Explanation:

Step1: Apply Zero-Product Property

If \(ab = 0\), then either \(a = 0\) or \(b = 0\). So for \((2x - 16)(x^2 - 49)=0\), we set each factor equal to zero:

1. \(2x - 16 = 0\)
2. \(x^2 - 49 = 0\)

Step2: Solve \(2x - 16 = 0\)

Add 16 to both sides: \(2x=16\)
Divide by 2: \(x = \frac{16}{2}=8\)

Step3: Solve \(x^2 - 49 = 0\)

Rewrite as \(x^2=49\)
Take square roots: \(x=\pm\sqrt{49}=\pm7\)

Answer:

8, -7, 7