Q. 431 - Intermediate Algebra

Question

In the following exercises, solve.

$144m^2-25=0$

Step-by-Step Solution

Answer

Answer is $m=\frac{5}{12},m=-\frac{5}{12}$

Step 1. Given

The equation is $144m^2-25=0$

Step 2. Simplify the equation

We will use $a^2-b^2=(a+b)(a-b)$ to simplify the equation.

$$\begin{gathered} 144m^2-25=0 \\ {\left(12m\right)}^2-{\left(5\right)}^2=0 \\ (12m+5)(12m-5)=0 \end{gathered}$$

So,

$$\begin{gathered} 12m+5=0 \\ m=-\frac{5}{12} \end{gathered}$$

and

$$\begin{gathered} 12m-5=0 \\ m=\frac{5}{12} \end{gathered}$$

Step 3. Check both the values

Put $m=\frac{5}{12}$ in original equation,

$$\begin{gathered} 144m^2-25=0 \\ 144{\left(\frac{5}{12}\right)}^2-25=0 \\ 25-25=0 \\ 0=0 \end{gathered}$$

True

Now put $m=\left(-\frac{5}{12}\right)$ in original equation,

$$\begin{gathered} 144m^2-25=0 \\ 144{\left(-\frac{5}{12}\right)}^2-25=0 \\ 25-25=0 \\ 0=0 \end{gathered}$$

True

Step 4. Required answer

Answer is $m=\frac{5}{12},m=-\frac{5}{12}$