Solve by Factoring square root of 5-x-3=0

$\sqrt{5 - x} - 3 = 0$

Step 1

Add $3$ to both sides of the equation.

$\sqrt{5 - x} = 3$

Step 2

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

${\sqrt{5 - x}}^{2} = 3^{2}$

Step 3

Simplify each side of the equation.

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

${({(5 - x)}^{\frac{1}{2}})}^{2} = 3^{2}$

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, ${(a^{m})}^{n} = a^{m n}$ .

${(5 - x)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 - x)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(5 - x)}^{1} = 3^{2}$

Simplify.

$5 - x = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$5 - x = 9$

Step 4

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$- x = 9 - 5$

Subtract $5$ from $9$ .

$- x = 4$

Divide each term in $- x = 4$ by $- 1$ and simplify.

Divide each term in $- x = 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{4}{- 1}$

Simplify the right side.

Divide $4$ by $- 1$ .

$x = - 4$