Question

solving quadratics by factoring
score: 0/5 penalty: 0.25 off
question
solve for all values of x by factoring.
x² + 2x - 4 = -4
answer attempt 1 out of 2
additional solution no solution
x =
submit answer

Explanation:

Step1: Simplify the equation

First, we add 4 to both sides of the equation \(x^{2}+2x - 4=-4\) to get it in standard form.
\(x^{2}+2x - 4 + 4=-4 + 4\)
Simplifying both sides, we have \(x^{2}+2x=0\)

Step2: Factor the quadratic

We factor out the greatest common factor, which is \(x\), from the left - hand side of the equation \(x^{2}+2x = 0\).
Using the distributive property \(ab+ac=a(b + c)\) (where \(a = x\), \(b=x\), and \(c = 2\)), we get \(x(x + 2)=0\)

Step3: Solve for x

According to the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
So, for \(x(x + 2)=0\), we have two cases:

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

Answer:

The solutions are \(x = 0\) and \(x=-2\)