Question

Solve each equation. Check your solutions.

$24+x^2=10x$

Short answer

The solution of$24+x^2=10$ is $\mathit{x}\mathbf{=}\mathbf{4}\mathbf{,}\mathbf{6}$.

Step-by-step solution

Step 1. Subtract.

Subtract $10x$from both the sides of the given equation.

role="math" localid="1647952589882" $$\begin{gathered} 24+x^2-10x=10x-10x \\ =0 \end{gathered}$$

Step 2. Factor by using GCF.

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

$\left(x-4\right)\left(x-6\right)=0$

Step 3. Write zero product property.

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

Step 4. Apply zero product property.

Apply zero product property to the given equation, $\left(x-4\right)\left(x-6\right)=0$.

$$\begin{gathered} x-4=0\text{or}x-6=0 \\ x=4x=6 \end{gathered}$$

Therefore, the roots are 4 and 6.

Step 5. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute 4 for$x$and 6 for$x$in the given equation and simplify.

role="math" localid="1647952986538" $$\begin{gathered} 24+{\left(4\right)}^2\stackrel{?}{=}10\left(4\right) \\ 40=40 \\ LHS=RHS \end{gathered}$$

role="math" localid="1647952992003" $$\begin{gathered} 24+{\left(6\right)}^2\stackrel{?}{=}10\left(6\right) \\ 60=60 \\ LHS=RHS \end{gathered}$$

Therefore, the obtained solution is correct.