Question

values of x by factoring.\\(x^2 + 2x = -2x\\)

Explanation:

Step1: Move all terms to left side

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

Step2: Factor the left - hand side

We can factor out the greatest common factor of \(x^{2}\) and \(4x\), which is \(x\). Using the distributive property \(ab + ac=a(b + c)\) (where \(a = x\), \(b=x\), and \(c = 4\)), we get:
\(x(x + 4)=0\)

Step3: Solve for x

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

• Case 1: \(x=0\)
• Case 2: \(x + 4=0\), which gives \(x=-4\)

Answer:

The solutions are \(x = 0\) and \(x=-4\)