# Solve for θ in Degrees 6tan(theta)^2-10tan(theta)+1=-5tan(theta)

Solve for θ in Degrees 6tan(theta)^2-10tan(theta)+1=-5tan(theta)
Add to both sides of the equation.
Factor by grouping.
Reorder terms.
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 .
Add to 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 .
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 positive in the first and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
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 .
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 .
Add to 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 .
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 positive in the first and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
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 .
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
Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
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### Name

Name one billion nine hundred fifty-one million four hundred ninety thousand eight hundred seventy-two

### Interesting facts

• 1951490872 has 32 divisors, whose sum is 6598470600
• The reverse of 1951490872 is 2780941591
• Previous prime number is 541

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 46
• Digital Root 1

### Name

Name eight hundred sixty-two million seven hundred seventy-one thousand nine hundred seventy-four

### Interesting facts

• 862771974 has 32 divisors, whose sum is 1786444800
• The reverse of 862771974 is 479177268
• Previous prime number is 349

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 51
• Digital Root 6

### Name

Name four hundred sixty-five million three hundred ninety-one thousand one hundred seventy-seven

### Interesting facts

• 465391177 has 8 divisors, whose sum is 485847936
• The reverse of 465391177 is 771193564
• Previous prime number is 5737

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 43
• Digital Root 7