Solve for x square root of -4x=100

$\sqrt{- 4 x} = 100$

Step 1

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

${\sqrt{- 4 x}}^{2} = 100^{2}$

Step 2

Simplify each side of the equation.

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

${({(- 4 x)}^{\frac{1}{2}})}^{2} = 100^{2}$

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, ${(a^{m})}^{n} = a^{m n}$ .

${(- 4 x)}^{\frac{1}{2} \cdot 2} = 100^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(- 4 x)}^{\frac{1}{2} \cdot 2} = 100^{2}$

Rewrite the expression.

${(- 4 x)}^{1} = 100^{2}$

Simplify.

$- 4 x = 100^{2}$

Simplify the right side.

Raise $100$ to the power of $2$ .

$- 4 x = 10000$

Step 3

Divide each term in $- 4 x = 10000$ by $- 4$ and simplify.

Divide each term in $- 4 x = 10000$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{10000}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{10000}{- 4}$

Divide $x$ by $1$ .

$x = \frac{10000}{- 4}$

Simplify the right side.

Divide $10000$ by $- 4$ .

$x = - 2500$