Question

you only have 2 questions left to raise your score.
question
solve for all values of x by factoring.
x² + 3x = -4x
answer attempt 1 out of 2
additional solution no solution
x =

Explanation:

Step1: Move all terms to left

First, we need to get all terms on one side of the equation. Add \(4x\) to both sides of the equation \(x^{2}+3x = - 4x\). So we have \(x^{2}+3x + 4x=0\), which simplifies to \(x^{2}+7x = 0\).

Step2: Factor the quadratic

Now, we factor out the greatest common factor from the left - hand side. The greatest common factor of \(x^{2}\) and \(7x\) is \(x\). So we can factor the equation as \(x(x + 7)=0\).

Step3: Apply the zero - product property

According to the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). So for \(x(x + 7)=0\), we set each factor equal to zero:

• If \(x=0\), then the equation is satisfied.
• If \(x + 7=0\), we solve for \(x\) by subtracting 7 from both sides, and we get \(x=-7\).

Answer:

\(x = 0\) or \(x=-7\)