Solve for x - square root of x=5

$- \sqrt{x} = 5$

Step 1

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

${(- \sqrt{x})}^{2} = 5^{2}$

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

Apply the product rule to $- x^{\frac{1}{2}}$ .

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

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

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

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

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

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

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

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

$x^{1} = 5^{2}$

Simplify.

$x = 5^{2}$

Simplify the right side.

Raise $5$ to the power of $2$ .

$x = 25$

Step 3

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

$No solution$