Solve for x square root of 4-x+5=2

$\sqrt{4 - x} + 5 = 2$

Move all terms not containing $\sqrt{4 - x}$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$\sqrt{4 - x} = 2 - 5$

Subtract $5$ from $2$ .

$\sqrt{4 - x} = - 3$

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

${\sqrt{4 - x}}^{2} = {(- 3)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 - x}$ as ${(4 - x)}^{\frac{1}{2}}$ .

${({(4 - x)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

Simplify the left side.

Simplify ${({(4 - x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 - x)}^{\frac{1}{2}})}^{2}$ .

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

${(4 - x)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 - x)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Rewrite the expression.

${(4 - x)}^{1} = {(- 3)}^{2}$

Simplify.

$4 - x = {(- 3)}^{2}$

Simplify the right side.

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

$4 - x = 9$

Solve for $x$ .

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

Subtract $4$ from both sides of the equation.

$- x = 9 - 4$

Subtract $4$ from $9$ .

$- x = 5$

Divide each term in $- x = 5$ by $- 1$ and simplify.

Divide each term in $- x = 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{5}{- 1}$

Divide $x$ by $1$ .

$x = \frac{5}{- 1}$

Simplify the right side.

Divide $5$ by $- 1$ .

$x = - 5$

Exclude the solutions that do not make $\sqrt{4 - x} + 5 = 2$ true.

$No solution$