Question

solve for all values of x by factoring.
$x^{2}+2x=-2x$
answer attempt 1 out of 2
additional solution no solution
$x = $

Explanation:

Step1: Rearrange the equation

Add \(2x\) to both sides to get \(x^{2}+2x + 2x=0\), which simplifies to \(x^{2}+4x = 0\).

Step2: Factor out the common factor

Factor out \(x\) from the left - hand side: \(x(x + 4)=0\).

Step3: Use the zero - product property

If \(ab = 0\), then either \(a = 0\) or \(b = 0\). So \(x=0\) or \(x + 4=0\).

Step4: Solve for \(x\)

From \(x + 4=0\), we get \(x=-4\).

Answer:

\(x = 0,x=-4\)