Question

if x + 3 = 0, then x
if x + 4 = 0, then x
x² + 7x + 12 = 0 are x

1. x² + 2x - 8 = 0

Explanation:

Step1: Factor the quadratic equation

We need to factor \(x^{2}+2x - 8 = 0\). We look for two numbers that multiply to \(- 8\) and add up to \(2\). The numbers are \(4\) and \(-2\) since \(4\times(-2)=-8\) and \(4+( - 2)=2\). So we can write the equation as \((x + 4)(x-2)=0\)

Step2: Solve for \(x\)

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

• For \(x + 4=0\), we get \(x=-4\)
• For \(x - 2=0\), we get \(x = 2\)

Answer:

The solutions of the equation \(x^{2}+2x - 8=0\) are \(x=-4\) and \(x = 2\)