Trigonometry Examples

Solve for @VAR z^4+4 square root of 2z^2+16=0
Step 1
Substitute into the equation. This will make the quadratic formula easy to use.
Step 2
Use the quadratic formula to find the solutions.
Step 3
Substitute the values , , and into the quadratic formula and solve for .
Step 4
Simplify.
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Step 4.1
Simplify the numerator.
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Step 4.1.1
Apply the product rule to .
Step 4.1.2
Raise to the power of .
Step 4.1.3
Rewrite as .
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Step 4.1.3.1
Use to rewrite as .
Step 4.1.3.2
Apply the power rule and multiply exponents, .
Step 4.1.3.3
Combine and .
Step 4.1.3.4
Cancel the common factor of .
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Step 4.1.3.4.1
Cancel the common factor.
Step 4.1.3.4.2
Rewrite the expression.
Step 4.1.3.5
Evaluate the exponent.
Step 4.1.4
Multiply by .
Step 4.1.5
Multiply .
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Step 4.1.5.1
Multiply by .
Step 4.1.5.2
Multiply by .
Step 4.1.6
Subtract from .
Step 4.1.7
Rewrite as .
Step 4.1.8
Rewrite as .
Step 4.1.9
Rewrite as .
Step 4.1.10
Rewrite as .
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Step 4.1.10.1
Factor out of .
Step 4.1.10.2
Rewrite as .
Step 4.1.11
Pull terms out from under the radical.
Step 4.1.12
Move to the left of .
Step 4.2
Multiply by .
Step 4.3
Simplify .
Step 5
The final answer is the combination of both solutions.
Step 6
Substitute the real value of back into the solved equation.
Step 7
Solve the first equation for .
Step 8
Solve the equation for .
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Step 8.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 8.2
The complete solution is the result of both the positive and negative portions of the solution.
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Step 8.2.1
First, use the positive value of the to find the first solution.
Step 8.2.2
Next, use the negative value of the to find the second solution.
Step 8.2.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 9
Solve the second equation for .
Step 10
Solve the equation for .
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Step 10.1
Remove parentheses.
Step 10.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 10.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 10.3.1
First, use the positive value of the to find the first solution.
Step 10.3.2
Next, use the negative value of the to find the second solution.
Step 10.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 11
The solution to is .