Q. 6.89 - Intermediate Algebra

Question

Solve, $3c^2=10c-8$

Step-by-Step Solution

Answer

The value is $c=\frac{4}{3},2$

Step 1: Given information

Given the equation $3c^2=10c-8$

Step 2: Writing in standard form

Writing in standard form, we get

$$\begin{gathered} 3c^2=10c-8 \\ 3c^2-10c+8=0 \\ 3c^2-6c-4c+8=0 \\ 3c(c-2)-4(c-2)=0 \\ (3c-4)(c-2)=0 \\ c=\frac{4}{3},2 \end{gathered}$$

Step 3: Checking the value

Substituting the value and checking, we get

$$\begin{gathered} 3c^2=10c-8 \\ 3{\left(\frac{4}{3}\right)}^2=10\left(\frac{4}{3}\right)-8 \\ \frac{16}{3}=\frac{16}{3} \end{gathered}$$

This is true

Step 4: Checking another value

Checking the value, we get

$$\begin{gathered} 3c^2=10c-8 \\ 3{\left(2\right)}^2=10\left(2\right)-8 \\ 12=20-8 \\ 12=12 \end{gathered}$$

This is true