Chapter 12.1, Problem 41WE

To determine

To solve: The equation $7a^3-175a=0$ by factoring.

Answer to Problem 41WE

The solution set is $\left(5\sqrt{7},-5\sqrt{7}\right)$ .

Explanation of Solution

Given information:

The given equation $7a^3-175a=0$ .

Calculation:

  $\begin{array}{l}\Rightarrow 7a^3-175a=0\\ \Rightarrow 7a\left(a^2-175\right)=0\\ \Rightarrow \frac{7a\left(a^2-175\right)}{7a}=\frac{0}{7a}\end{array}$

(Divide by 7a on both sides)

  $\begin{array}{l}\Rightarrow \left(a^2-175\right)=0\\ \Rightarrow a^2-175=0\\ \Rightarrow a^2-175+175=0+175\end{array}$

(Adding 175 on both sides)

  $\begin{array}{l}\Rightarrow a^2=175\\ \Rightarrow a=\pm \sqrt{175}\\ \Rightarrow a=\pm 5\sqrt{7}\\ \Rightarrow a=5\sqrt{7};a=5\sqrt{7}\end{array}$

Therefore, the solution set is $\left(5\sqrt{7},-5\sqrt{7}\right)$ .