Trigonometry Examples

Find the Intersection of the Functions f(x) = square root of 3x^2-8+6 , f(x)=8
,
Step 1
Substitute for .
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Solve for .
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Step 2.2.1
Add and .
Step 2.2.2
Move all terms not containing to the right side of the equation.
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Step 2.2.2.1
Add to both sides of the equation.
Step 2.2.2.2
Add and .
Step 2.3
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2.4
Simplify each side of the equation.
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Step 2.4.1
Use to rewrite as .
Step 2.4.2
Simplify the left side.
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Step 2.4.2.1
Simplify .
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Step 2.4.2.1.1
Multiply the exponents in .
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Step 2.4.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.4.2.1.1.2
Cancel the common factor of .
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Step 2.4.2.1.1.2.1
Cancel the common factor.
Step 2.4.2.1.1.2.2
Rewrite the expression.
Step 2.4.2.1.2
Simplify.
Step 2.4.3
Simplify the right side.
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Step 2.4.3.1
Raise to the power of .
Step 2.5
Solve for .
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Step 2.5.1
Divide each term in by and simplify.
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Step 2.5.1.1
Divide each term in by .
Step 2.5.1.2
Simplify the left side.
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Step 2.5.1.2.1
Cancel the common factor of .
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Step 2.5.1.2.1.1
Cancel the common factor.
Step 2.5.1.2.1.2
Divide by .
Step 2.5.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.5.3
Simplify .
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Step 2.5.3.1
Rewrite as .
Step 2.5.3.2
Simplify the numerator.
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Step 2.5.3.2.1
Rewrite as .
Step 2.5.3.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.5.3.3
Multiply by .
Step 2.5.3.4
Combine and simplify the denominator.
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Step 2.5.3.4.1
Multiply by .
Step 2.5.3.4.2
Raise to the power of .
Step 2.5.3.4.3
Raise to the power of .
Step 2.5.3.4.4
Use the power rule to combine exponents.
Step 2.5.3.4.5
Add and .
Step 2.5.3.4.6
Rewrite as .
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Step 2.5.3.4.6.1
Use to rewrite as .
Step 2.5.3.4.6.2
Apply the power rule and multiply exponents, .
Step 2.5.3.4.6.3
Combine and .
Step 2.5.3.4.6.4
Cancel the common factor of .
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Step 2.5.3.4.6.4.1
Cancel the common factor.
Step 2.5.3.4.6.4.2
Rewrite the expression.
Step 2.5.3.4.6.5
Evaluate the exponent.
Step 2.5.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.5.4.1
First, use the positive value of the to find the first solution.
Step 2.5.4.2
Next, use the negative value of the to find the second solution.
Step 2.5.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form: