Solve for x square root of x-2+3=-2

$\sqrt{x - 2 + 3} = - 2$

Step 1

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

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

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 2 + 3}$ as ${(x - 2 + 3)}^{\frac{1}{2}}$ .

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

Simplify the left side.

Simplify ${({(x - 2 + 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x - 2 + 3)}^{\frac{1}{2}})}^{2}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Add $- 2$ and $3$ .

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

Simplify.

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

Simplify the right side.

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

$x + 1 = 4$

Step 3

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

Subtract $1$ from both sides of the equation.

$x = 4 - 1$

Subtract $1$ from $4$ .

$x = 3$

Step 4

Exclude the solutions that do not make $\sqrt{x - 2 + 3} = - 2$ true.

$No solution$