Question

Solve each equation. Check your solution.

$10+2\sqrt{x}=0$

Short answer

There is no solution of the given equation.

Check:

Substitute 25 for x in the given equation $10+2\sqrt{x}=0$.

$$\begin{gathered} 10+2\sqrt{x}=0 \\ 10+2\sqrt{25}\underset{¯}{\underset{¯}{?}}0 \\ \text{10+2}\left(5\right)\underset{¯}{\underset{¯}{?}}0 \\ \text{10+10}\underset{¯}{\underset{¯}{?}}0 \\ \text{20}\ne 0 \end{gathered}$$

Therefore,$x=25$ is not the solution of the given equation $10+2\sqrt{x}=0$.

Step-by-step solution

Step 1. Rewrite the given equation.

The given equation can be written as:

$$\begin{gathered} 10+2\sqrt{x}=0 \\ 2\sqrt{x}=-10 \\ \sqrt{x}=-\frac{10}{2} \\ \sqrt{x}=-5 \end{gathered}$$

Step 2. Solve the given equation.

The solution of the given equation is:

$$\begin{gathered} {\left(\sqrt{x}\right)}^2={\left(-5\right)}^2\left(\text{squaringbothsides}\right) \\ x=25 \end{gathered}$$

Therefore, the value of x is 25.

Step 3. Check the solution.

Substitute 25 for x in the given equation $10+2\sqrt{x}=0$.

$$\begin{gathered} 10+2\sqrt{x}=0 \\ 10+2\sqrt{25}\underset{¯}{\underset{¯}{?}}0 \\ \text{10+2}\left(5\right)\underset{¯}{\underset{¯}{?}}0 \\ \text{10+10}\underset{¯}{\underset{¯}{?}}0 \\ \text{20}\ne 0 \end{gathered}$$

Therefore,$x=25$ is not the solution of the given equation $10+2\sqrt{x}=0$.