Finite Math Examples

${(6 - x)}^{2} = 13$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$6 - x = \pm \sqrt{13}$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$6 - x = \sqrt{13}$

Step 2.2

Subtract $6$ from both sides of the equation.

$- x = \sqrt{13} - 6$

Step 2.3

Divide each term in $- x = \sqrt{13} - 6$ by $- 1$ and simplify.

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Step 2.3.1

Divide each term in $- x = \sqrt{13} - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\sqrt{13}}{- 1} + \frac{- 6}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\sqrt{13}}{- 1} + \frac{- 6}{- 1}$

Step 2.3.2.2

Divide $x$ by $1$ .

$x = \frac{\sqrt{13}}{- 1} + \frac{- 6}{- 1}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Move the negative one from the denominator of $\frac{\sqrt{13}}{- 1}$ .

$x = - 1 \cdot \sqrt{13} + \frac{- 6}{- 1}$

Step 2.3.3.1.2

Rewrite $- 1 \cdot \sqrt{13}$ as $- \sqrt{13}$ .

$x = - \sqrt{13} + \frac{- 6}{- 1}$

Step 2.3.3.1.3

Divide $- 6$ by $- 1$ .

$x = - \sqrt{13} + 6$

Step 2.4

Next, use the negative value of the $\pm$ to find the second solution.

$6 - x = - \sqrt{13}$

Step 2.5

Subtract $6$ from both sides of the equation.

$- x = - \sqrt{13} - 6$

Step 2.6

Divide each term in $- x = - \sqrt{13} - 6$ by $- 1$ and simplify.

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Step 2.6.1

Divide each term in $- x = - \sqrt{13} - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- \sqrt{13}}{- 1} + \frac{- 6}{- 1}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- \sqrt{13}}{- 1} + \frac{- 6}{- 1}$

Step 2.6.2.2

Divide $x$ by $1$ .

$x = \frac{- \sqrt{13}}{- 1} + \frac{- 6}{- 1}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Simplify each term.

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Step 2.6.3.1.1

Dividing two negative values results in a positive value.

$x = \frac{\sqrt{13}}{1} + \frac{- 6}{- 1}$

Step 2.6.3.1.2

Divide $\sqrt{13}$ by $1$ .

$x = \sqrt{13} + \frac{- 6}{- 1}$

Step 2.6.3.1.3

Divide $- 6$ by $- 1$ .

$x = \sqrt{13} + 6$

Step 2.7

The complete solution is the result of both the positive and negative portions of the solution.

$x = - \sqrt{13} + 6, \sqrt{13} + 6$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt{13} + 6, \sqrt{13} + 6$

Decimal Form:

$x = 2.39444872 \dots, 9.60555127 \dots$