Pre-Algebra Examples

Solve for x x^4-13x^2=-36
Step 1
Add to both sides of the equation.
Step 2
Factor the left side of the equation.
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Step 2.1
Rewrite as .
Step 2.2
Let . Substitute for all occurrences of .
Step 2.3
Factor using the AC method.
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Step 2.3.1
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 2.3.2
Write the factored form using these integers.
Step 2.4
Replace all occurrences of with .
Step 2.5
Rewrite as .
Step 2.6
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.7
Rewrite as .
Step 2.8
Factor.
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Step 2.8.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.8.2
Remove unnecessary parentheses.
Step 3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4
Set equal to and solve for .
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Step 4.1
Set equal to .
Step 4.2
Subtract from both sides of the equation.
Step 5
Set equal to and solve for .
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Step 5.1
Set equal to .
Step 5.2
Add to both sides of the equation.
Step 6
Set equal to and solve for .
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Step 6.1
Set equal to .
Step 6.2
Subtract from both sides of the equation.
Step 7
Set equal to and solve for .
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Step 7.1
Set equal to .
Step 7.2
Add to both sides of the equation.
Step 8
The final solution is all the values that make true.