Trigonometry Examples

$8 q^{2} - 6 q = 7 q^{2} - 9 q + 10$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $7 q^{2}$ from both sides of the equation.

$8 q^{2} - 6 q - 7 q^{2} = - 9 q + 10$

Step 1.2

Add $9 q$ to both sides of the equation.

$8 q^{2} - 6 q - 7 q^{2} + 9 q = 10$

Step 1.3

Subtract $7 q^{2}$ from $8 q^{2}$ .

$q^{2} - 6 q + 9 q = 10$

Step 1.4

Add $- 6 q$ and $9 q$ .

$q^{2} + 3 q = 10$

Step 2

Subtract $10$ from both sides of the equation.

$q^{2} + 3 q - 10 = 0$

Step 3

Factor $q^{2} + 3 q - 10$ using the AC method.

Tap for more steps...

Step 3.1

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 $- 10$ and whose sum is $3$ .

$- 2, 5$

Step 3.2

Write the factored form using these integers.

$(q - 2) (q + 5) = 0$

Step 4

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

$q - 2 = 0$

$q + 5 = 0$

Step 5

Set $q - 2$ equal to $0$ and solve for $q$ .

Tap for more steps...

Step 5.1

Set $q - 2$ equal to $0$ .

$q - 2 = 0$

Step 5.2

Add $2$ to both sides of the equation.

$q = 2$

Step 6

Set $q + 5$ equal to $0$ and solve for $q$ .

Tap for more steps...

Step 6.1

Set $q + 5$ equal to $0$ .

$q + 5 = 0$

Step 6.2

Subtract $5$ from both sides of the equation.

$q = - 5$

Step 7

The final solution is all the values that make $(q - 2) (q + 5) = 0$ true.

$q = 2, - 5$