Q24. - Algebra 1

Question

Solve each equation. Check your solutions.

$x^2-3x-18=0$

Step-by-Step Solution

Answer

The solution of $x^2-3x-18=0$ is $\mathit{x}\mathbf{=}\mathbf{6}\mathbf{,}\mathbf{-}\mathbf{3}$.

Step 1. Factor by using GCF.

Factor by using GCF to get the form $xy=0$.

$\left(x-6\right)\left(x+3\right)=0$

Step 2. Write zero product property.

For any real numbers $x$ and $x$, if $xy=0$ then $x=0,y=0$ or both $x$ and $y$ equal to zero.

Step 3. Apply zero product property.

Apply zero product property to the given equation, $\left(x-6\right)\left(x+3\right)=0$.

$$\begin{gathered} x-6=0\text{ or }x+3=0 \\ x=6x=-3 \end{gathered}$$

Therefore, the roots are 6 and $-3$.

Step 4. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute 6 for $x$ and $-3$ for $x$ in the given equation and simplify.
$$\begin{gathered} {\left(6\right)}^2-3\left(6\right)-18\stackrel{?}{=}0 \\ 36-18-18\stackrel{?}{=}0 \\ 0=0 \\ LHS=RHS \end{gathered}$$

$$\begin{gathered} {\left(-3\right)}^2-3\left(-3\right)\stackrel{?}{-18=}0 \\ 9+9-18\stackrel{?}{=}0 \\ 0=0 \\ LHS=RHS \end{gathered}$$

Therefore, the obtained solution is correct.