Chapter 11.5, Problem 64SR

To determine

To calculate: To solve the equation and check the solution

Answer to Problem 64SR

The solution of the equation is $x=22$

Explanation of Solution

Given information: Equation is $\sqrt{x+3}=-5$

Calculation:

Equation is given as

  $\sqrt{x+3}=-5$

On solving the above equation:

  $\begin{array}{l}{\left(\sqrt{x+3}\right)}^2={\left(-5\right)}^2\\ x+3=25\\ x=25-3\\ x=22\end{array}$

In order to check the solution, substitute $x=22$ in the equation:

Left hand side of equation is calculated as

  $\begin{array}{l}\Rightarrow \sqrt{22+3}\\ \Rightarrow \sqrt{25}\\ \Rightarrow \sqrt{5^2}\\ \Rightarrow \pm 5\\ \Rightarrow -5\end{array}$

Since, left hand side of equation is equal to right hand side of equation

Thus, $x=22$ is the solution

Conclusion:

Hence, $x=22$ is the solution of the equation