Trigonometry Examples

Solve for x |x-15|=x^2-15x
Step 1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2
Rewrite the equation as .
Step 3
Remove the absolute value term. This creates a on the right side of the equation because .
Step 4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 4.1
First, use the positive value of the to find the first solution.
Step 4.2
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.3
Move all terms containing to the left side of the equation.
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Step 4.3.1
Subtract from both sides of the equation.
Step 4.3.2
Subtract from .
Step 4.4
Add to both sides of the equation.
Step 4.5
Factor using the AC method.
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Step 4.5.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 4.5.2
Write the factored form using these integers.
Step 4.6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.7
Set equal to and solve for .
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Step 4.7.1
Set equal to .
Step 4.7.2
Add to both sides of the equation.
Step 4.8
Set equal to and solve for .
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Step 4.8.1
Set equal to .
Step 4.8.2
Add to both sides of the equation.
Step 4.9
The final solution is all the values that make true.
Step 4.10
Next, use the negative value of the to find the second solution.
Step 4.11
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.12
Simplify .
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Step 4.12.1
Rewrite.
Step 4.12.2
Simplify by adding zeros.
Step 4.12.3
Apply the distributive property.
Step 4.12.4
Multiply by .
Step 4.13
Move all terms containing to the left side of the equation.
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Step 4.13.1
Subtract from both sides of the equation.
Step 4.13.2
Subtract from .
Step 4.14
Add to both sides of the equation.
Step 4.15
Factor the left side of the equation.
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Step 4.15.1
Factor out of .
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Step 4.15.1.1
Factor out of .
Step 4.15.1.2
Factor out of .
Step 4.15.1.3
Rewrite as .
Step 4.15.1.4
Factor out of .
Step 4.15.1.5
Factor out of .
Step 4.15.2
Factor.
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Step 4.15.2.1
Factor using the AC method.
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Step 4.15.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 4.15.2.1.2
Write the factored form using these integers.
Step 4.15.2.2
Remove unnecessary parentheses.
Step 4.16
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.17
Set equal to and solve for .
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Step 4.17.1
Set equal to .
Step 4.17.2
Add to both sides of the equation.
Step 4.18
Set equal to and solve for .
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Step 4.18.1
Set equal to .
Step 4.18.2
Subtract from both sides of the equation.
Step 4.19
The final solution is all the values that make true.
Step 4.20
The complete solution is the result of both the positive and negative portions of the solution.
Step 5
Exclude the solutions that do not make true.