Q 6.97 - Intermediate Algebra

Question

Solve, $8x^3=24x^2-18x$

Step-by-Step Solution

Answer

The value is $x=\frac{3}{2}$

Step 1: Given information

Given the equation $8x^3=24x^2-18x$

Step 2: Bring all terms to one side and solve

Bringing to one side, we get

$$\begin{gathered} 8x^3=24x^2-18x \\ 8x^3-24x^2+18x=0 \\ x(8x^2-24x+18)=0 \end{gathered}$$

Step 3: Using the zero factor property calculate the value

Using zero factor property

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

Step 4: Checking the value

Substituting, we get

$$\begin{gathered} 8{\left(\frac{3}{2}\right)}^3=24{\left(\frac{3}{2}\right)}^2-18\left(\frac{3}{2}\right) \\ 8\times \frac{27}{8}=24\times \frac{9}{4}-27 \\ 27=54-27 \\ 27=27 \end{gathered}$$

So its correct