Trigonometry Examples

${(r + 18)}^{2} = r^{2} + 24^{2}$

Step 1

Raise $24$ to the power of $2$ .

${(r + 18)}^{2} = r^{2} + 576$

Step 2

Move all terms containing $r$ to the left side of the equation.

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Step 2.1

Subtract $r^{2}$ from both sides of the equation.

${(r + 18)}^{2} - r^{2} = 576$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite ${(r + 18)}^{2}$ as $(r + 18) (r + 18)$ .

$(r + 18) (r + 18) - r^{2} = 576$

Step 2.2.2

Expand $(r + 18) (r + 18)$ using the FOIL Method.

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Step 2.2.2.1

Apply the distributive property.

$r (r + 18) + 18 (r + 18) - r^{2} = 576$

Step 2.2.2.2

Apply the distributive property.

$r \cdot r + r \cdot 18 + 18 (r + 18) - r^{2} = 576$

Step 2.2.2.3

Apply the distributive property.

$r \cdot r + r \cdot 18 + 18 r + 18 \cdot 18 - r^{2} = 576$

Step 2.2.3

Simplify and combine like terms.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Multiply $r$ by $r$ .

$r^{2} + r \cdot 18 + 18 r + 18 \cdot 18 - r^{2} = 576$

Step 2.2.3.1.2

Move $18$ to the left of $r$ .

$r^{2} + 18 \cdot r + 18 r + 18 \cdot 18 - r^{2} = 576$

Step 2.2.3.1.3

Multiply $18$ by $18$ .

$r^{2} + 18 r + 18 r + 324 - r^{2} = 576$

Step 2.2.3.2

Add $18 r$ and $18 r$ .

$r^{2} + 36 r + 324 - r^{2} = 576$

Step 2.3

Combine the opposite terms in $r^{2} + 36 r + 324 - r^{2}$ .

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Step 2.3.1

Subtract $r^{2}$ from $r^{2}$ .

$36 r + 324 + 0 = 576$

Step 2.3.2

Add $36 r + 324$ and $0$ .

$36 r + 324 = 576$

Step 3

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

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Step 3.1

Subtract $324$ from both sides of the equation.

$36 r = 576 - 324$

Step 3.2

Subtract $324$ from $576$ .

$36 r = 252$

Step 4

Divide each term in $36 r = 252$ by $36$ and simplify.

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Step 4.1

Divide each term in $36 r = 252$ by $36$ .

$\frac{36 r}{36} = \frac{252}{36}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $36$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{36 r}{36} = \frac{252}{36}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r = \frac{252}{36}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $252$ by $36$ .

$r = 7$