Finite Math Examples

Solve for x |x^2+2x-15|=|x-3|
Step 1
Rewrite the equation as .
Step 2
Rewrite the absolute value equation as four equations without absolute value bars.
Step 3
After simplifying, there are only two unique equations to be solved.
Step 4
Solve for .
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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
Subtract from .
Step 4.3
Add to both sides of the equation.
Step 4.4
Add and .
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
Subtract from both sides of the equation.
Step 4.9
The final solution is all the values that make true.
Step 5
Solve for .
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Step 5.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 5.2
Simplify .
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Step 5.2.1
Rewrite.
Step 5.2.2
Simplify by adding zeros.
Step 5.2.3
Apply the distributive property.
Step 5.2.4
Simplify.
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Step 5.2.4.1
Multiply by .
Step 5.2.4.2
Multiply by .
Step 5.3
Move all terms containing to the left side of the equation.
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Step 5.3.1
Subtract from both sides of the equation.
Step 5.3.2
Subtract from .
Step 5.4
Add to both sides of the equation.
Step 5.5
Add and .
Step 5.6
Factor the left side of the equation.
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Step 5.6.1
Factor out of .
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Step 5.6.1.1
Factor out of .
Step 5.6.1.2
Factor out of .
Step 5.6.1.3
Rewrite as .
Step 5.6.1.4
Factor out of .
Step 5.6.1.5
Factor out of .
Step 5.6.2
Factor.
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Step 5.6.2.1
Factor using the AC method.
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Step 5.6.2.1.1
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 5.6.2.1.2
Write the factored form using these integers.
Step 5.6.2.2
Remove unnecessary parentheses.
Step 5.7
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 5.8
Set equal to and solve for .
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Step 5.8.1
Set equal to .
Step 5.8.2
Add to both sides of the equation.
Step 5.9
Set equal to and solve for .
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Step 5.9.1
Set equal to .
Step 5.9.2
Subtract from both sides of the equation.
Step 5.10
The final solution is all the values that make true.
Step 6
List all of the solutions.