Solve by Factoring square root of 5x=-5

$\sqrt{5 x} = - 5$

Step 1

Add $5$ to both sides of the equation.

$\sqrt{5 x} + 5 = 0$

Step 2

Subtract $5$ from both sides of the equation.

$\sqrt{5 x} = - 5$

Step 3

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{5 x}}^{2} = {(- 5)}^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x}$ as ${(5 x)}^{\frac{1}{2}}$ .

${({(5 x)}^{\frac{1}{2}})}^{2} = {(- 5)}^{2}$

Simplify the left side.

Simplify ${({(5 x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 x)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(5 x)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 x)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Rewrite the expression.

${(5 x)}^{1} = {(- 5)}^{2}$

Simplify.

$5 x = {(- 5)}^{2}$

Simplify the right side.

Raise $- 5$ to the power of $2$ .

$5 x = 25$

Step 5

Divide each term in $5 x = 25$ by $5$ and simplify.

Divide each term in $5 x = 25$ by $5$ .

$\frac{5 x}{5} = \frac{25}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{25}{5}$

Divide $x$ by $1$ .

$x = \frac{25}{5}$

Simplify the right side.

Divide $25$ by $5$ .

$x = 5$

Step 6

Exclude the solutions that do not make $\sqrt{5 x} + 5 = 0$ true.

$No solution$