Finite Math Examples

${(x^{2} - 10)}^{2} - 121 = 0$

Step 1

Add $121$ to both sides of the equation.

${(x^{2} - 10)}^{2} = 121$

Step 2

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

$x^{2} - 10 = \pm \sqrt{121}$

Step 3

Simplify $\pm \sqrt{121}$ .

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Step 3.1

Rewrite $121$ as $11^{2}$ .

$x^{2} - 10 = \pm \sqrt{11^{2}}$

Step 3.2

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

$x^{2} - 10 = \pm 11$

Step 4

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

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Step 4.1

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

$x^{2} - 10 = 11$

Step 4.2

Move all terms not containing $x$ to the right side of the equation.

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Step 4.2.1

Add $10$ to both sides of the equation.

$x^{2} = 11 + 10$

Step 4.2.2

Add $11$ and $10$ .

$x^{2} = 21$

Step 4.3

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

$x = \pm \sqrt{21}$

Step 4.4

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

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Step 4.4.1

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

$x = \sqrt{21}$

Step 4.4.2

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

$x = - \sqrt{21}$

Step 4.4.3

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

$x = \sqrt{21}, - \sqrt{21}$

Step 4.5

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

$x^{2} - 10 = - 11$

Step 4.6

Move all terms not containing $x$ to the right side of the equation.

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Step 4.6.1

Add $10$ to both sides of the equation.

$x^{2} = - 11 + 10$

Step 4.6.2

Add $- 11$ and $10$ .

$x^{2} = - 1$

Step 4.7

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

$x = \pm \sqrt{- 1}$

Step 4.8

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i$

Step 4.9

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

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Step 4.9.1

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

$x = i$

Step 4.9.2

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

$x = - i$

Step 4.9.3

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

$x = i, - i$

Step 4.10

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

$x = \sqrt{21}, - \sqrt{21}, i, - i$