Trigonometry Examples

a^{2} + 21^{2} = 29^{2}

$a^{2} + 21^{2} = 29^{2}$

Step 1

Raise

21

$21$ to the power of

2

$2$ .

a^{2} + 441 = 29^{2}

$a^{2} + 441 = 29^{2}$

Step 2

Raise

29

$29$ to the power of

2

$2$ .

a^{2} + 441 = 841

$a^{2} + 441 = 841$

Step 3

Move all terms not containing

a

$a$ to the right side of the equation.

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Step 3.1

Subtract

441

$441$ from both sides of the equation.

a^{2} = 841 - 441

$a^{2} = 841 - 441$

Step 3.2

Subtract

441

$441$ from

841

$841$ .

a^{2} = 400

$a^{2} = 400$

a^{2} = 400

$a^{2} = 400$

Step 4

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

a = \pm \sqrt{400}

$a = \pm \sqrt{400}$

Step 5

Simplify

\pm \sqrt{400}

$\pm \sqrt{400}$ .

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Step 5.1

Rewrite

400

$400$ as

20^{2}

$20^{2}$ .

a = \pm \sqrt{20^{2}}

$a = \pm \sqrt{20^{2}}$

Step 5.2

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

a = \pm 20

$a = \pm 20$

a = \pm 20

$a = \pm 20$

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

$\pm$ to find the first solution.

a = 20

$a = 20$

Step 6.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

a = - 20

$a = - 20$

Step 6.3

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

a = 20, - 20

$a = 20, - 20$

a = 20, - 20

$a = 20, - 20$