Q. 302 - Intermediate Algebra

Question

In the following exercises, solve:

$3y^2-18y=-27$

Step-by-Step Solution

Answer

On solving the equation, we get $y=3$.

Step 1. Given information.

Consider the given equation,

$3y^2-18y=-27$

Write the quadratic equation in standard form,

$3y^2-18y+27=0$

Step 2. Factor the quadratic expression.

On factoring, we get,

$$\begin{gathered} 3y^2-9y-9y+27=0 \\ 3y\left(y-3\right)-9\left(y-3\right)=0 \\ \left(y-3\right)\left(3y-9\right)=0 \\ 3\left(y-3\right)\left(y-3\right)=0 \\ {\left(y-3\right)}^2=0 \end{gathered}$$

Use the zero product property,

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

Step 3. Check the answers.

Substitute $y=3$ in the given equation,

$$\begin{gathered} 3{\left(3\right)}^2-18\left(3\right)=-27 \\ 27-54=-27 \\ -27=-27 \end{gathered}$$

This is true.

Hence, the answer is $y=3$.