Q 289 - Intermediate Algebra

Question

In the following exercises, solve:

$49m^2=144$

Step-by-Step Solution

Answer

On solving the equation, we get $m=\frac{12}{7},-\frac{12}{7}$.

Step 1. Given information.

Consider the given equation,

$49m^2=144$

Write the quadratic equation in standard form,

$49m^2-144=0$

Step 2. Factor the quadratic expression.

On factoring, we get,

$$\begin{gathered} {\left(7m\right)}^2-{\left(12\right)}^2=0 \\ \left(7m+12\right)\left(7m-12\right)=0 \end{gathered}$$

Use the zero product property,

$$\begin{gathered} 7m+12=0 \\ m=-\frac{12}{7} \end{gathered}$$

Then,

$$\begin{gathered} 7m-12=0 \\ m=\frac{12}{7} \end{gathered}$$

Step 3. Check the answers.

Substitute $m=\frac{12}{7}$ in the given equation,

$$\begin{gathered} 49{\left(\frac{12}{7}\right)}^2=144 \\ 49\times \frac{144}{49}=144 \\ 144=144 \end{gathered}$$

This is true.

Substitute $m=-\frac{12}{7}$ in the given equation,

$$\begin{gathered} 49{\left(-\frac{12}{7}\right)}^2=144 \\ 49\times \frac{144}{49}=144 \\ 144=144 \end{gathered}$$

This is also true.

Hence, the answer is $m=\frac{12}{7},-\frac{12}{7}$.