Trigonometry Examples

$r (r + 7) - 78 = 0$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$r \cdot r + r \cdot 7 - 78 = 0$

Step 1.2

Multiply $r$ by $r$ .

$r^{2} + r \cdot 7 - 78 = 0$

Step 1.3

Move $7$ to the left of $r$ .

$r^{2} + 7 r - 78 = 0$

Step 2

Factor $r^{2} + 7 r - 78$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 78$ and whose sum is $7$ .

$- 6, 13$

Step 2.2

Write the factored form using these integers.

$(r - 6) (r + 13) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$r - 6 = 0$

$r + 13 = 0$

Step 4

Set $r - 6$ equal to $0$ and solve for $r$ .

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Step 4.1

Set $r - 6$ equal to $0$ .

$r - 6 = 0$

Step 4.2

Add $6$ to both sides of the equation.

$r = 6$

Step 5

Set $r + 13$ equal to $0$ and solve for $r$ .

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Step 5.1

Set $r + 13$ equal to $0$ .

$r + 13 = 0$

Step 5.2

Subtract $13$ from both sides of the equation.

$r = - 13$

Step 6

The final solution is all the values that make $(r - 6) (r + 13) = 0$ true.

$r = 6, - 13$