Question

Solve the equation by factoring. \(x^{2}+3 x-31=-3\)

Short answer

The solution to the equation is \(x=4\) and \(x=-7\)

Step-by-step solution

Transform the equation

First, transform the equation to a classic quadratic form by moving all terms to one side so you get \(x^{2}+3x-31+3=0\)

Simplify

Simplify the equation to get the quadratic equation as \(x^{2}+3x-28=0\)

Factorize

Next step is to factorize \(x^{2}+3x-28\). We are looking for two numbers that multiply to -28 and add up to 3. The numbers that fit these requirements are 7 and -4. Therefore, we have \((x-4)(x+7)=0\) as the factorized form.

Solve for x

Finally, equate each factor to zero and solve for x: \(x-4=0 \Rightarrow x=4\) and \(x+7=0 \Rightarrow x=-7\)