Algebra Examples

Solve for x 8x^3+12x^2+6x+1=0
Step 1
Factor the left side of the equation.
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Step 1.1
Regroup terms.
Step 1.2
Rewrite as .
Step 1.3
Rewrite as .
Step 1.4
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Step 1.5
Simplify.
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Step 1.5.1
Apply the product rule to .
Step 1.5.2
Raise to the power of .
Step 1.5.3
Multiply by .
Step 1.5.4
Multiply by .
Step 1.5.5
One to any power is one.
Step 1.6
Factor out of .
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Step 1.6.1
Factor out of .
Step 1.6.2
Factor out of .
Step 1.6.3
Factor out of .
Step 1.7
Factor out of .
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Step 1.7.1
Factor out of .
Step 1.7.2
Factor out of .
Step 1.8
Add and .
Step 1.9
Factor using the perfect square rule.
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Step 1.9.1
Rewrite as .
Step 1.9.2
Rewrite as .
Step 1.9.3
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 1.9.4
Rewrite the polynomial.
Step 1.9.5
Factor using the perfect square trinomial rule , where and .
Step 2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3
Set equal to and solve for .
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Step 3.1
Set equal to .
Step 3.2
Solve for .
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Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Divide each term in by and simplify.
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Step 3.2.2.1
Divide each term in by .
Step 3.2.2.2
Simplify the left side.
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Step 3.2.2.2.1
Cancel the common factor of .
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Step 3.2.2.2.1.1
Cancel the common factor.
Step 3.2.2.2.1.2
Divide by .
Step 3.2.2.3
Simplify the right side.
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Step 3.2.2.3.1
Move the negative in front of the fraction.
Step 4
The final solution is all the values that make true.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: