Q. 601 - Intermediate Algebra

Question

In the following exercises, solve.

$\sqrt{x+5}+1=x$

Step-by-Step Solution

Answer

The solution of the equation is $x=-1 or 4$

Step 1. Given Information

We have $$\begin{gathered} \sqrt{x+5}+1=x \\ \sqrt{x+5}=x-1 \end{gathered}$$

Step 2. Squaring both sides

$$\begin{gathered} {\left(\sqrt{x+5}\right)}^2={\left(x-1\right)}^2 \\ x+5={\left(x-1\right)}^2 \end{gathered}$$

Step 3. Simplify the equation

$$\begin{gathered} x+5=x^2-2x+1 \\ {x}^2-3x-4=0 \end{gathered}$$

Step 4. Factorize the equation

$$\begin{gathered} x^2-4x+x-4=0 \\ x\left(x-4\right)+1\left(x-4\right)=0 \\ \left(x+1\right)\left(x-4\right)=0 \\ x=-1,4 \end{gathered}$$