Trigonometry Examples

$r (r - 18) = - 81$

Step 1

Simplify $r (r - 18)$ .

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Step 1.1

Apply the distributive property.

$r \cdot r + r \cdot - 18 = - 81$

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $r$ by $r$ .

$r^{2} + r \cdot - 18 = - 81$

Step 1.2.2

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

$r^{2} - 18 r = - 81$

Step 2

Add $81$ to both sides of the equation.

$r^{2} - 18 r + 81 = 0$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $81$ as $9^{2}$ .

$r^{2} - 18 r + 9^{2} = 0$

Step 3.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$18 r = 2 \cdot r \cdot 9$

Step 3.3

Rewrite the polynomial.

$r^{2} - 2 \cdot r \cdot 9 + 9^{2} = 0$

Step 3.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = r$ and $b = 9$ .

${(r - 9)}^{2} = 0$

Step 4

Set the $r - 9$ equal to $0$ .

$r - 9 = 0$

Step 5

Add $9$ to both sides of the equation.

$r = 9$