# Solve for θ in Degrees 8tan(theta)^2+10tan(theta)+10=7

Solve for θ in Degrees 8tan(theta)^2+10tan(theta)+10=7
Subtract from both sides of the equation.
Subtract from .
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Move the negative in front of the fraction.
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
Evaluate .
The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
The resulting angle of is positive and coterminal with .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
Subtract from .
List the new angles.
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Move the negative in front of the fraction.
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
Evaluate .
The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
The resulting angle of is positive and coterminal with .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
Subtract from .
List the new angles.
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
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### Name

Name one billion seventy-two million four hundred nine thousand seven hundred twenty

### Interesting facts

• 1072409720 has 64 divisors, whose sum is 4347219456
• The reverse of 1072409720 is 0279042701
• Previous prime number is 1151

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 32
• Digital Root 5

### Name

Name one billion nine hundred six million four hundred fifty-five thousand four hundred sixty-eight

### Interesting facts

• 1906455468 has 16 divisors, whose sum is 5719366440
• The reverse of 1906455468 is 8645546091
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 48
• Digital Root 3

### Name

Name one billion eight hundred seventy-nine million five hundred thirty-one thousand five hundred twenty

### Interesting facts

• 1879531520 has 32768 divisors, whose sum is 438961762944
• The reverse of 1879531520 is 0251359781
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 41
• Digital Root 5