Chapter 10.4, Problem 26P

Solve each radical equation. Check your solution. If there is no solution, write no solution. $x=\sqrt{3x+28}$

To determine

To find: the solution of the equation.

Answer to Problem 26P

The solution of the equation is $x=-4,7$ .

Explanation of Solution

Given information:

The equation is $x=\sqrt{3x+28}$ .

Calculation: to find the solution of the equation, first square and then simplify,

  $\begin{array}{l}x=\sqrt{3x+28}\\ x^2=3x+28\text{ [square]}\\ x^2-3x-28=0\text{ [simplify]}\\ \left(x-7\right)\left(x+4\right)\text{=0 [factorise]}\\ x=-4,7\end{array}$

Thus, the solution of the equation is $x=-4,7$ .

To check the solution substitute $x=-4,7$ , in the equation,

  $\begin{array}{l}x=\sqrt{3x+28}\\ 7=\sqrt{3\left(7\right)+28}\text{ [substitute }x=7\text{]}\\ 7=7\text{ [simplify]}\\ -4=\sqrt{3\left(-4\right)+28}\text{ [substitute }x=-4\text{]}\\ -4=-4\text{ [simplify]}\end{array}$