Q. 294 - Intermediate Algebra

Question

In the following exercises, solve:

$100y^2=9$

Step-by-Step Solution

Answer

On solving the equation, we get $y=\frac{3}{10},-\frac{3}{10}$.

Step 1. Given information.

Consider the given equation,

$100y^2=9$

Write the quadratic equation in standard form,

$100y^2-9=0$

Step 2. Factor the quadratic expression.

On factoring, we get,

$$\begin{gathered} {\left(10y\right)}^2-3^2=0 \\ \left(10y+3\right)\left(10y-3\right)=0 \end{gathered}$$

Use the zero product property,

$$\begin{gathered} 10y+3=0 \\ y=-\frac{3}{10} \end{gathered}$$

Then,

$$\begin{gathered} 10y-3=0 \\ y=\frac{3}{10} \end{gathered}$$

Step 3. Check the answers.

Substitute $y=-\frac{3}{10}$ in the given equation,

$$\begin{gathered} 100{\left(\frac{3}{10}\right)}^2=9 \\ 100\times \frac{9}{100}=9 \\ 9=9 \end{gathered}$$

This is true.

Substitute $y=-\frac{3}{10}$ in the given equation,

$$\begin{gathered} 100{\left(-\frac{3}{10}\right)}^2=9 \\ 100\times \frac{9}{100}=9 \\ 9=9 \end{gathered}$$

This is also true.

Hence, the answer is $y=\frac{3}{10},-\frac{3}{10}$.