Pre-Algebra Examples

$- {(\sqrt{x - 4})}^{2} = 0$

Step 1

Simplify $- {\sqrt{x - 4}}^{2}$ .

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Step 1.1

Rewrite ${\sqrt{x - 4}}^{2}$ as $x - 4$ .

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Step 1.1.1

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

$- {({(x - 4)}^{\frac{1}{2}})}^{2} = 0$

Step 1.1.2

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

$- {(x - 4)}^{\frac{1}{2} \cdot 2} = 0$

Step 1.1.3

Combine $\frac{1}{2}$ and $2$ .

$- {(x - 4)}^{\frac{2}{2}} = 0$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Cancel the common factor.

$- {(x - 4)}^{\frac{2}{2}} = 0$

Step 1.1.4.2

Rewrite the expression.

$- {(x - 4)}^{1} = 0$

Step 1.1.5

Simplify.

$- (x - 4) = 0$

Step 1.2

Apply the distributive property.

$- x - - 4 = 0$

Step 1.3

Multiply $- 1$ by $- 4$ .

$- x + 4 = 0$

Step 2

Subtract $4$ from both sides of the equation.

$- x = - 4$

Step 3

Divide each term in $- x = - 4$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Step 3.2.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 4$ by $- 1$ .

$x = 4$