Trigonometry Examples

Solve for x 9(x-4)^2+16(y-3)^2=144
Step 1
Subtract from both sides of the equation.
Step 2
Simplify .
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Step 2.1
Simplify each term.
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Step 2.1.1
Rewrite as .
Step 2.1.2
Expand using the FOIL Method.
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Step 2.1.2.1
Apply the distributive property.
Step 2.1.2.2
Apply the distributive property.
Step 2.1.2.3
Apply the distributive property.
Step 2.1.3
Simplify and combine like terms.
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Step 2.1.3.1
Simplify each term.
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Step 2.1.3.1.1
Multiply by .
Step 2.1.3.1.2
Move to the left of .
Step 2.1.3.1.3
Multiply by .
Step 2.1.3.2
Subtract from .
Step 2.1.4
Apply the distributive property.
Step 2.1.5
Simplify.
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Step 2.1.5.1
Multiply by .
Step 2.1.5.2
Multiply by .
Step 2.2
Combine the opposite terms in .
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Step 2.2.1
Subtract from .
Step 2.2.2
Add and .
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Simplify each term.
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Step 3.3.1.1
Move the negative in front of the fraction.
Step 3.3.1.2
Cancel the common factor of and .
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Step 3.3.1.2.1
Factor out of .
Step 3.3.1.2.2
Cancel the common factors.
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Step 3.3.1.2.2.1
Factor out of .
Step 3.3.1.2.2.2
Cancel the common factor.
Step 3.3.1.2.2.3
Rewrite the expression.
Step 4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5
Simplify .
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Step 5.1
To write as a fraction with a common denominator, multiply by .
Step 5.2
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 5.2.1
Multiply by .
Step 5.2.2
Multiply by .
Step 5.3
Combine the numerators over the common denominator.
Step 5.4
Simplify the numerator.
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Step 5.4.1
Factor out of .
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Step 5.4.1.1
Factor out of .
Step 5.4.1.2
Factor out of .
Step 5.4.1.3
Factor out of .
Step 5.4.2
Multiply by .
Step 5.5
Rewrite as .
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Step 5.5.1
Factor the perfect power out of .
Step 5.5.2
Factor the perfect power out of .
Step 5.5.3
Rearrange the fraction .
Step 5.6
Pull terms out from under the radical.
Step 5.7
Raise to the power of .
Step 5.8
Combine and .
Step 6
The complete solution is the result of both the positive and negative portions of the solution.
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Step 6.1
First, use the positive value of the to find the first solution.
Step 6.2
Add to both sides of the equation.
Step 6.3
Next, use the negative value of the to find the second solution.
Step 6.4
Add to both sides of the equation.
Step 6.5
The complete solution is the result of both the positive and negative portions of the solution.