Trigonometry Examples

Solve for a ( square root of 74(2-a))/(v((2-a)^2+(3-b)^2))=5
Step 1
Factor each term.
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Step 1.1
Rewrite as .
Step 1.2
Expand using the FOIL Method.
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Step 1.2.1
Apply the distributive property.
Step 1.2.2
Apply the distributive property.
Step 1.2.3
Apply the distributive property.
Step 1.3
Simplify and combine like terms.
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Step 1.3.1
Simplify each term.
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Step 1.3.1.1
Multiply by .
Step 1.3.1.2
Multiply by .
Step 1.3.1.3
Multiply by .
Step 1.3.1.4
Rewrite using the commutative property of multiplication.
Step 1.3.1.5
Multiply by by adding the exponents.
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Step 1.3.1.5.1
Move .
Step 1.3.1.5.2
Multiply by .
Step 1.3.1.6
Multiply by .
Step 1.3.1.7
Multiply by .
Step 1.3.2
Subtract from .
Step 1.4
Rewrite as .
Step 1.5
Expand using the FOIL Method.
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Step 1.5.1
Apply the distributive property.
Step 1.5.2
Apply the distributive property.
Step 1.5.3
Apply the distributive property.
Step 1.6
Simplify and combine like terms.
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Step 1.6.1
Simplify each term.
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Step 1.6.1.1
Multiply by .
Step 1.6.1.2
Multiply by .
Step 1.6.1.3
Multiply by .
Step 1.6.1.4
Rewrite using the commutative property of multiplication.
Step 1.6.1.5
Multiply by by adding the exponents.
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Step 1.6.1.5.1
Move .
Step 1.6.1.5.2
Multiply by .
Step 1.6.1.6
Multiply by .
Step 1.6.1.7
Multiply by .
Step 1.6.2
Subtract from .
Step 1.7
Add and .
Step 2
Find the LCD of the terms in the equation.
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Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
The LCM of one and any expression is the expression.
Step 3
Multiply each term in by to eliminate the fractions.
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Step 3.1
Multiply 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
Rewrite the expression.
Step 3.2.2
Apply the distributive property.
Step 3.2.3
Move to the left of .
Step 3.3
Simplify the right side.
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Step 3.3.1
Apply the distributive property.
Step 3.3.2
Simplify.
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Step 3.3.2.1
Rewrite using the commutative property of multiplication.
Step 3.3.2.2
Move to the left of .
Step 3.3.2.3
Rewrite using the commutative property of multiplication.
Step 3.3.3
Apply the distributive property.
Step 3.3.4
Simplify.
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Step 3.3.4.1
Multiply by .
Step 3.3.4.2
Multiply by .
Step 3.3.4.3
Multiply by .
Step 3.3.5
Remove parentheses.
Step 4
Solve the equation.
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Step 4.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.2
Move all terms containing to the left side of the equation.
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Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Multiply .
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Step 4.2.2.1
Multiply by .
Step 4.2.2.2
Multiply by .
Step 4.3
Subtract from both sides of the equation.
Step 4.4
Use the quadratic formula to find the solutions.
Step 4.5
Substitute the values , , and into the quadratic formula and solve for .
Step 4.6
Simplify.
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Step 4.6.1
Simplify the numerator.
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Step 4.6.1.1
Apply the distributive property.
Step 4.6.1.2
Multiply by .
Step 4.6.1.3
Add parentheses.
Step 4.6.1.4
Let . Substitute for all occurrences of .
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Step 4.6.1.4.1
Rewrite as .
Step 4.6.1.4.2
Expand using the FOIL Method.
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Step 4.6.1.4.2.1
Apply the distributive property.
Step 4.6.1.4.2.2
Apply the distributive property.
Step 4.6.1.4.2.3
Apply the distributive property.
Step 4.6.1.4.3
Simplify and combine like terms.
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Step 4.6.1.4.3.1
Simplify each term.
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Step 4.6.1.4.3.1.1
Rewrite using the commutative property of multiplication.
Step 4.6.1.4.3.1.2
Multiply by by adding the exponents.
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Step 4.6.1.4.3.1.2.1
Move .
Step 4.6.1.4.3.1.2.2
Multiply by .
Step 4.6.1.4.3.1.3
Multiply by .
Step 4.6.1.4.3.1.4
Combine using the product rule for radicals.
Step 4.6.1.4.3.1.5
Multiply by .
Step 4.6.1.4.3.1.6
Rewrite as .
Step 4.6.1.4.3.1.7
Pull terms out from under the radical, assuming positive real numbers.
Step 4.6.1.4.3.2
Reorder the factors of .
Step 4.6.1.4.3.3
Subtract from .
Step 4.6.1.5
Factor out of .
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Step 4.6.1.5.1
Factor out of .
Step 4.6.1.5.2
Factor out of .
Step 4.6.1.5.3
Factor out of .
Step 4.6.1.5.4
Factor out of .
Step 4.6.1.5.5
Factor out of .
Step 4.6.1.5.6
Factor out of .
Step 4.6.1.5.7
Factor out of .
Step 4.6.1.6
Replace all occurrences of with .
Step 4.6.1.7
Simplify.
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Step 4.6.1.7.1
Simplify each term.
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Step 4.6.1.7.1.1
Remove parentheses.
Step 4.6.1.7.1.2
Apply the distributive property.
Step 4.6.1.7.1.3
Simplify.
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Step 4.6.1.7.1.3.1
Rewrite using the commutative property of multiplication.
Step 4.6.1.7.1.3.2
Rewrite using the commutative property of multiplication.
Step 4.6.1.7.1.3.3
Rewrite using the commutative property of multiplication.
Step 4.6.1.7.1.4
Simplify each term.
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Step 4.6.1.7.1.4.1
Multiply by by adding the exponents.
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Step 4.6.1.7.1.4.1.1
Move .
Step 4.6.1.7.1.4.1.2
Multiply by .
Step 4.6.1.7.1.4.2
Multiply by by adding the exponents.
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Step 4.6.1.7.1.4.2.1
Move .
Step 4.6.1.7.1.4.2.2
Multiply by .
Step 4.6.1.7.1.4.3
Multiply by by adding the exponents.
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Step 4.6.1.7.1.4.3.1
Move .
Step 4.6.1.7.1.4.3.2
Multiply by .
Step 4.6.1.7.1.5
Apply the distributive property.
Step 4.6.1.7.1.6
Simplify.
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Step 4.6.1.7.1.6.1
Multiply by .
Step 4.6.1.7.1.6.2
Multiply by .
Step 4.6.1.7.1.6.3
Multiply by .
Step 4.6.1.7.1.6.4
Multiply by .
Step 4.6.1.7.1.7
Remove parentheses.
Step 4.6.1.7.1.8
Apply the distributive property.
Step 4.6.1.7.1.9
Simplify.
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Step 4.6.1.7.1.9.1
Multiply by .
Step 4.6.1.7.1.9.2
Multiply by .
Step 4.6.1.7.1.9.3
Multiply by .
Step 4.6.1.7.1.9.4
Multiply by .
Step 4.6.1.7.1.10
Remove parentheses.
Step 4.6.1.7.2
Combine the opposite terms in .
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Step 4.6.1.7.2.1
Add and .
Step 4.6.1.7.2.2
Add and .
Step 4.6.1.7.3
Subtract from .
Step 4.6.2
Multiply by .
Step 4.7
The final answer is the combination of both solutions.