Q 6.95 - Intermediate Algebra

Question

Solve $18a^2-30=-33a$

Step-by-Step Solution

Answer

The value is $a=\frac{2}{3},\frac{-5}{2}$

Step 1: Given information

Given the equation, $18a^2-30=-33a$

Step 2: Writing in standard form

Writing in standard form, we get

$$\begin{gathered} 18a^2-30=-33a \\ 18a^2+33a-30=0 \\ 3(6a^2+11a-10)=0 \end{gathered}$$

Step 3: Using zero factor principle

Using the principle, we get

$$\begin{gathered} 6a^2+11a-10=0 \\ 6a^2+15a-4a-10=0 \\ 3a(2a+5)-2(2a+5)=0 \\ (3a-2)(2a+5)=0 \\ a=\frac{2}{3},-\frac{5}{2} \end{gathered}$$

Step 4: Checking the value

Substituting and checking the value, we get

$$\begin{gathered} 18{\left(\frac{2}{3}\right)}^2-30=-33\left(\frac{2}{3}\right) \\ 18\times \frac{4}{9}-30=-22 \\ 8-30=-22 \\ -22=-22 \end{gathered}$$

This is true

Step 5: Checking for another value

Checking, we get

$$\begin{gathered} 18{\left(\frac{-5}{2}\right)}^2-30=-33\left(\frac{-5}{2}\right) \\ 18\times \frac{25}{4}-30=\frac{165}{2} \\ \frac{165}{2}=\frac{165}{2} \end{gathered}$$

This is true