Question

question
solve for all values of x by factoring.
x² - 4x = -5x
answer attempt 1 out of 2
additional solution no solution
x =
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Explanation:

Step1: Move all terms to left

To solve the equation \(x^{2}-4x = - 5x\) by factoring, first, we move all terms to the left - hand side of the equation. We add \(5x\) to both sides of the equation:
\(x^{2}-4x + 5x=0\)
Simplify the left - hand side: \(x^{2}+x = 0\)

Step2: Factor the left - hand side

We factor out the greatest common factor (GCF) from the terms \(x^{2}\) and \(x\). The GCF of \(x^{2}\) and \(x\) is \(x\). So we can factor the left - hand side as:
\(x(x + 1)=0\)

Step3: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). In our factored form \(x(x + 1)=0\), we set each factor equal to zero and solve for \(x\):

• Case 1: If \(x=0\), then the equation is satisfied.
• Case 2: If \(x + 1=0\), we solve for \(x\) by subtracting 1 from both sides of the equation. We get \(x=-1\)

Answer:

\(x = 0\) or \(x=-1\)