# Solve for x 10cos(x)^2+5cos(x)-5=0

Solve for x 10cos(x)^2+5cos(x)-5=0
Factor the left side of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Let . Substitute for all occurrences of .
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 .
Multiply by .
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, .
Factor.
Replace all occurrences of with .
Remove unnecessary parentheses.
Replace the left side with the factored expression.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Simplify .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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 radians in both directions.
, for any integer
, for any integer
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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 radians in both directions.
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
, for any integer
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### Name

Name six hundred eighty-two million three hundred fifty-five thousand eight hundred forty-five

### Interesting facts

• 682355845 has 4 divisors, whose sum is 818827020
• The reverse of 682355845 is 548553286
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 46
• Digital Root 1

### Name

Name eight hundred fifty-nine million eight hundred ninety-three thousand forty-four

### Interesting facts

• 859893044 has 8 divisors, whose sum is 1934759358
• The reverse of 859893044 is 440398958
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 50
• Digital Root 5

### Name

Name six hundred thirty-eight million six hundred sixty-one thousand four hundred eighty-two

### Interesting facts

• 638661482 has 8 divisors, whose sum is 958785636
• The reverse of 638661482 is 284166836
• Previous prime number is 1213

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 44
• Digital Root 8