Q18. - Algebra 1

Question

Solve each equation. Check your solution.

$a^2=15a$

Step-by-Step Solution

Answer

The solution of $a^2=15a$ is $a=0,\frac{1}{2}$.

Step 1. Subtract.

Subtract $15a$ from both the sides of the given equation.

 $$\begin{gathered} a^2-15a=15a-15a \\ =0 \end{gathered}$$

Step 2. Factor by using GCF.

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

$a\left(a-15\right)=0$

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, $a\left(a-15\right)=0$.

 $$\begin{gathered} a=0\text{ or }a-15=0 \\ a=15 \end{gathered}$$

Therefore, the roots are 0 and 15.

Step 5. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute 0 for $a$ and for in the given equation and simplify.

 $$\begin{gathered} 0^2\stackrel{?}{=}15\cdot 0 \\ 0=0 \\ LHS=RHS \end{gathered}$$

$$\begin{gathered} {15}^2\stackrel{?}{=}15\cdot 15 \\ 225=225 \\ LHS=RHS \end{gathered}$$

Therefore, the obtained solution is correct.