Solve for x 1+ square root of x+2=0

$1 + \sqrt{x + 2} = 0$

Subtract $1$ from both sides of the equation.

$\sqrt{x + 2} = - 1$

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $- 1$ to the power of $2$ .

$x + 2 = 1$

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

Subtract $2$ from both sides of the equation.

$x = 1 - 2$

Subtract $2$ from $1$ .

$x = - 1$

Exclude the solutions that do not make $1 + \sqrt{x + 2} = 0$ true.

$No solution$