Q. 301 - Intermediate Algebra

Question

In the following exercises, solve:

$20x^2-60x=-45$

Step-by-Step Solution

Answer

On solving the equation, we get $x=\frac{3}{2}$.

Step 1. Given information.

Consider the given equation,

$20x^2-60x=-45$

Write the quadratic equation in standard form,

$20x^2-60x+45=0$

Step 2. Factor the quadratic expression.

On factoring, we get,

$$\begin{gathered} 5\left(4x^2-12x+9\right)=0 \\ 4x^2-6x-6x+9=0 \\ 2x\left(2x-3\right)-3\left(2x-3\right)=0 \\ {\left(2x-3\right)}^2=0 \end{gathered}$$

Use the zero product property,

$$\begin{gathered} 2x-3=0 \\ x=\frac{3}{2} \end{gathered}$$

Step 3. Check the answers.

Substitute $x=\frac{3}{2}$ in the given equation,

$$\begin{gathered} 20{\left(\frac{3}{2}\right)}^2-60\left(\frac{3}{2}\right)=-45 \\ 20\times \frac{9}{4}-90=-45 \\ 45-90=-45 \\ -45=-45 \end{gathered}$$

This is true.

Hence, the answer is $x=\frac{3}{2}$.