Chapter 10, Problem 13CR

To determine

To solve the equation.

Answer to Problem 13CR

  $x=4$ or $x=-1$

Explanation of Solution

Given information: $x=\sqrt{3x+4}$

Formula Used:Factorization

Calculation:

  $x=\sqrt{3x+4}$

So, squaring both sides

  ${\left(x\right)}^2={\left(\sqrt{3x+4}\right)}^2$

Now,

  $x^2=3x+4$

So,

  $x^2-3x-4=0$

Now,

  $x^2+x-4x-4=0$

So,

  $x\left(x+1\right)-4\left(x+1\right)=0$

Now,

  $\left(x-4\right)\left(x+1\right)=0$

Hence,

  $x=4$ or $x=-1$