Basic Math Examples

$36 = \sqrt{39^{2}} - {(r - 6)}^{2}$

Step 1

Rewrite the equation as $\sqrt{39^{2}} - {(r - 6)}^{2} = 36$ .

$\sqrt{39^{2}} - {(r - 6)}^{2} = 36$

Step 2

Subtract $\sqrt{39^{2}}$ from both sides of the equation.

$- {(r - 6)}^{2} = 36 - \sqrt{39^{2}}$

Step 3

Simplify $36 - \sqrt{39^{2}}$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Pull terms out from under the radical, assuming positive real numbers.

$- {(r - 6)}^{2} = 36 - 1 \cdot 39$

Step 3.1.2

Multiply $- 1$ by $39$ .

$- {(r - 6)}^{2} = 36 - 39$

Step 3.2

Subtract $39$ from $36$ .

$- {(r - 6)}^{2} = - 3$

Step 4

Divide each term in $- {(r - 6)}^{2} = - 3$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- {(r - 6)}^{2} = - 3$ by $- 1$ .

$\frac{- {(r - 6)}^{2}}{- 1} = \frac{- 3}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{{(r - 6)}^{2}}{1} = \frac{- 3}{- 1}$

Step 4.2.2

Divide ${(r - 6)}^{2}$ by $1$ .

${(r - 6)}^{2} = \frac{- 3}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 3$ by $- 1$ .

${(r - 6)}^{2} = 3$

Step 5

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

$r - 6 = \pm \sqrt{3}$

Step 6

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

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Step 6.1

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

$r - 6 = \sqrt{3}$

Step 6.2

Add $6$ to both sides of the equation.

$r = \sqrt{3} + 6$

Step 6.3

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

$r - 6 = - \sqrt{3}$

Step 6.4

Add $6$ to both sides of the equation.

$r = - \sqrt{3} + 6$

Step 6.5

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

$r = \sqrt{3} + 6, - \sqrt{3} + 6$

Step 7

The result can be shown in multiple forms.

Exact Form:

$r = \sqrt{3} + 6, - \sqrt{3} + 6$

Decimal Form:

$r = 7.73205080 \dots, 4.26794919 \dots$