Question

solve each equation by factoring.

1. ( x^2 - 10x = -16 )

Explanation:

Step1: Rewrite in standard form

Move all terms to the left side: \(x^{2}-10x + 16=0\)

Step2: Factor the quadratic

Find two numbers that multiply to \(16\) and add to \(- 10\). The numbers are \(-2\) and \(-8\). So, \(x^{2}-10x + 16=(x - 2)(x - 8)=0\)

Step3: Solve for x

Set each factor equal to zero:
\(x - 2 = 0\) gives \(x = 2\)
\(x - 8 = 0\) gives \(x = 8\)

Answer:

\(x = 2\) or \(x = 8\)