Question

Solve:

$x^2-x-12=0$

Short answer

The solutions of the quadratic equations $x^2-x-12=0$are $x=4,-3$

Step-by-step solution

Step 1. Given Information

An equation:

$x^2-x-12=0$

Step 2. Factor the quadratic expression

Factorize the equation,

$$\begin{gathered} x^2-x-12=0 \\ (x-4)(x+3)=0 \end{gathered}$$

Step 3. Use the Zero-Product property

Use the Zero Product Property and set each factor to zero.

$$\begin{gathered} x-4=0 \\ x=4 \\ x+3=0 \\ x=-3 \end{gathered}$$

The value of x is $x=4,-3$

Step 4. Check the answer

Check by substituting the values in the original equation,

When $x=4$,

$$\begin{gathered} {\left(4\right)}^2-\left(4\right)-12=0 \\ 16-4-12=0 \\ 16-16=0 \end{gathered}$$

When $x=-3$,

$$\begin{gathered} {(-3)}^2-(-3)-12=0 \\ 9+3-12=0 \\ 12-12=0 \end{gathered}$$

Hence the equation holds true.