Chapter 1.6, Problem 8MRE

To determine

To solve the equation:

  $x\cdot x=16$

Where, $x\in \left\{0,1,2,3,4,5,6\right\}$ .

Answer to Problem 8MRE

  $x=4$

Explanation of Solution

Given:

  $x\cdot x=16$

Concept Used:

• Steps to solve a linear equation:
1. Use distributive property to eliminate any grouping symbol.
2. Simplify the expression in each side of the equation.
3. Collect the variables on one side of the equation and the constants on the other side.
4. Isolate the variable
• To check the solution of an equation substitute the solution in the equation and check whether it satisfies.

Calculation:

In order to solve the equation:

  $x\cdot x=16$

First, simplify the expression in each side of the equation, as

  $\begin{array}{c}x\cdot x=16\\ \Rightarrow x^2=16\end{array}$

Now, isolate the variable by taking square root both sides.

  $\begin{array}{c}{x}^2=16\\ \Rightarrow x=\pm \sqrt{16}\\ \Rightarrow x=\pm 4\end{array}$

Now,

  $\begin{array}{l}x=4\in \left\{0,1,2,3,4,5,6\right\}\\ \text{But,}\\ x=-4\notin \left\{0,1,2,3,4,5,6\right\}\end{array}$

Thus, solution of given equation is $x=4$ , that satisfies condition

  $x\in \left\{0,1,2,3,4,5,6\right\}$ .