Q 288 - Intermediate Algebra

Question

In the following exercises, solve:

$12b^2-15b=-9b$

Step-by-Step Solution

Answer

On solving the equation, we get $b=0,\frac{1}{2}$.

Step 1. Given information.

Consider the given equation,

$12b^2-15b=-9b$

Write the quadratic equation in standard form,

$$\begin{gathered} 12b^2-15b+9b=0 \\ 12b^2-6b=0 \end{gathered}$$

Step 2. Factor the quadratic expression.

On factoring, we get,

$6b\left(2b-1\right)=0$

Use the zero product property,

$$\begin{gathered} 6b=0 \\ b=0 \end{gathered}$$

Then,

$$\begin{gathered} 2b-1=0 \\ 2b=1 \\ b=\frac{1}{2} \end{gathered}$$

Step 3. Check the answers.

Substitute $b=0$ in the given equation,

$$\begin{gathered} 12{\left(0\right)}^2-15\left(0\right)=-9\left(0\right) \\ 0=0 \end{gathered}$$

This is true.

Substitute $b=\frac{1}{2}$ in the given equation,

$$\begin{gathered} 12{\left(\frac{1}{2}\right)}^2-15\left(\frac{1}{2}\right)=-9\left(\frac{1}{2}\right) \\ 3-\frac{15}{2}=-\frac{9}{2} \\ -\frac{9}{2}=-\frac{9}{2} \end{gathered}$$

This is also true.

Hence, the answer is $b=0,\frac{1}{2}$.