Algebra Examples

$\sqrt{- 4 x} = 100$

Step 1

Subtract $100$ from both sides of the equation.

$\sqrt{- 4 x} - 100 = 0$

Step 2

Simplify each term.

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Step 2.1

Rewrite $- 4 x$ as $2^{2} \cdot (- 1 x)$ .

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Step 2.1.1

Factor $4$ out of $- 4$ .

$\sqrt{4 (- 1) x} - 100 = 0$

Step 2.1.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot - 1 x} - 100 = 0$

Step 2.1.3

Add parentheses.

$\sqrt{2^{2} \cdot (- 1 x)} - 100 = 0$

Step 2.2

Pull terms out from under the radical.

$2 \sqrt{- 1 x} - 100 = 0$

Step 3

Factor $2$ out of $2 \sqrt{- 1 x} - 100$ .

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Step 3.1

Factor $2$ out of $2 \sqrt{- 1 x}$ .

$2 (\sqrt{- 1 x}) - 100 = 0$

Step 3.2

Factor $2$ out of $- 100$ .

$2 \sqrt{- 1 x} + 2 \cdot - 50 = 0$

Step 3.3

Factor $2$ out of $2 \sqrt{- 1 x} + 2 \cdot - 50$ .

$2 (\sqrt{- 1 x} - 50) = 0$

Step 4

Divide each term in $2 (\sqrt{- 1 x} - 50) = 0$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 (\sqrt{- 1 x} - 50) = 0$ by $2$ .

$\frac{2 (\sqrt{- 1 x} - 50)}{2} = \frac{0}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 (\sqrt{- 1 x} - 50)}{2} = \frac{0}{2}$

Step 4.2.1.2

Divide $\sqrt{- 1 x} - 50$ by $1$ .

$\sqrt{- 1 x} - 50 = \frac{0}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $2$ .

$\sqrt{- 1 x} - 50 = 0$

Step 5

Add $50$ to both sides of the equation.

$\sqrt{- 1 x} = 50$

Step 6

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

${\sqrt{- 1 x}}^{2} = 50^{2}$

Step 7

Simplify each side of the equation.

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Step 7.1

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

${({(- 1 x)}^{\frac{1}{2}})}^{2} = 50^{2}$

Step 7.2

Simplify the left side.

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Step 7.2.1

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

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Step 7.2.1.1

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

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Step 7.2.1.1.1

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

${(- 1 x)}^{\frac{1}{2} \cdot 2} = 50^{2}$

Step 7.2.1.1.2

Cancel the common factor of $2$ .

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Step 7.2.1.1.2.1

Cancel the common factor.

${(- 1 x)}^{\frac{1}{2} \cdot 2} = 50^{2}$

Step 7.2.1.1.2.2

Rewrite the expression.

${(- 1 x)}^{1} = 50^{2}$

Step 7.2.1.2

Rewrite $- 1 x$ as $- x$ .

${(- x)}^{1} = 50^{2}$

Step 7.2.1.3

Simplify.

$- x = 50^{2}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Raise $50$ to the power of $2$ .

$- x = 2500$

Step 8

Divide each term in $- x = 2500$ by $- 1$ and simplify.

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Step 8.1

Divide each term in $- x = 2500$ by $- 1$ .

$\frac{- x}{- 1} = \frac{2500}{- 1}$

Step 8.2

Simplify the left side.

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Step 8.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{2500}{- 1}$

Step 8.2.2

Divide $x$ by $1$ .

$x = \frac{2500}{- 1}$

Step 8.3

Simplify the right side.

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Step 8.3.1

Divide $2500$ by $- 1$ .

$x = - 2500$