Q.7 - Intermediate Algebra

Question

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $4m^2=36$

Step-by-Step Solution

Answer

The solution of the quadratic equation: $m=3, m=-3$ 

Step 1. Given information

Consider the quadratic equation $4m^2=36$

The objective is to solve the quadratic equation by using the square root property. 

If $x^2=k$, then $x=\pm \sqrt{k}$

The quadratic term is isolated. Divide by 4 to make its coefficient 1. 

$$\begin{gathered} \frac{4m^2}{4}=\frac{36}{4} \\ m^2=9 \end{gathered}$$

Step 2. Apply square root property

So, $m=\pm \sqrt{9}$

Simplify the radical.   

$$\begin{gathered} m=\pm \sqrt{3·3} \\ m=\pm 3 \end{gathered}$$

Rewrite to show two solutions.    

$m=3, m=-3$

Step 3. Check the solutions

Substitute $m=3$ in the original equation.

$$\begin{gathered} 4m^2=36 \\ 4{\left(3\right)}^2\stackrel{?}{=}36 \\ 4\left(9\right)\stackrel{?}{=}36 \\ 36=36 \end{gathered}$$

Substitute $m=-3$in the original equation.

$$\begin{gathered} 4m^2=36 \\ 4{(-3)}^2\stackrel{?}{=}36 \\ 4\left(9\right)\stackrel{?}{=}36 \\ 36=36 \end{gathered}$$