Chapter 9.7, Problem 54CCR

To determine

To solve : the given equation.

Answer to Problem 54CCR

The solution of the given equation is $x=6$ .

Explanation of Solution

Given information :

The given equation:

  $-2x^3-100=-532$

Concept used:

By the definition of a cube root, if $x^3=y$ , then $x=\sqrt[3]{y}$ .

Calculation :

As per problem,

  $\begin{array}{l}-2x^3-100=-532\text{ [Write the equation]}\\ -2x^3-100+100=-532+100\text{ [Add 100 to each side]}\\ -2x^3=-432\text{ [Simplify]}\\ x^3=216\text{ [Divide both sides by }-2\text{]}\\ x=\sqrt[3]{216}\text{ [Definition of cube root]}\\ x=6\text{ [Check (}6\text{)}\cdot (6\text{)}\cdot (6\text{)}=216\text{]}\end{array}$

The solution of the given equation is $x=6$ .