# Solve for ? square root of 2cos(x)^2+cos(x)=0

Solve for ? square root of 2cos(x)^2+cos(x)=0
Factor the left side of the equation.
Factor out of .
Factor out of .
Multiply by .
Factor out of .
Replace the left side with the factored expression.
Factor out of .
Factor out of .
Raise to the power of .
Factor out of .
Factor out of .
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 .
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.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Move the negative in front of the fraction.
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.
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
The final solution is all the values that make true.
, for any integer
Consolidate and to .
, for any integer
Do you know how to Solve for ? square root of 2cos(x)^2+cos(x)=0? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

### Name

Name eight hundred seventy-two million four hundred thirty-five thousand one hundred thirty-four

### Interesting facts

• 872435134 has 8 divisors, whose sum is 1308885120
• The reverse of 872435134 is 431534278
• Previous prime number is 6113

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 37
• Digital Root 1

### Name

Name four hundred sixty-seven million one hundred fifty-four thousand four hundred eighteen

### Interesting facts

• 467154418 has 8 divisors, whose sum is 711190512
• The reverse of 467154418 is 814451764
• Previous prime number is 67

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 40
• Digital Root 4

### Name

Name two billion one hundred forty-five million six hundred seventy-six thousand one hundred ninety-two

### Interesting facts

• 2145676192 has 128 divisors, whose sum is 17774979552
• The reverse of 2145676192 is 2916765412
• Previous prime number is 11

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 43
• Digital Root 7