Solve the Rational Equation for x square root of x=-9

$\sqrt{x} = - 9$

Step 1

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

${\sqrt{x}}^{2} = {(- 9)}^{2}$

Step 2

Simplify each side of the equation.

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

${(x^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Simplify the left side.

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

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

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

$x^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Rewrite the expression.

$x^{1} = {(- 9)}^{2}$

Simplify.

$x = {(- 9)}^{2}$

Simplify the right side.

Raise $- 9$ to the power of $2$ .

$x = 81$

Step 3

Exclude the solutions that do not make $\sqrt{x} = - 9$ true.

$No solution$