Basic Math Examples

Solve for a a^2+b^2+2a-6b+10=0
Step 1
Use the quadratic formula to find the solutions.
Step 2
Substitute the values , , and into the quadratic formula and solve for .
Step 3
Simplify.
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Step 3.1
Simplify the numerator.
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Step 3.1.1
Raise to the power of .
Step 3.1.2
Multiply by .
Step 3.1.3
Apply the distributive property.
Step 3.1.4
Simplify.
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Step 3.1.4.1
Multiply by .
Step 3.1.4.2
Multiply by .
Step 3.1.5
Subtract from .
Step 3.1.6
Rewrite in a factored form.
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Step 3.1.6.1
Factor out of .
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Step 3.1.6.1.1
Factor out of .
Step 3.1.6.1.2
Factor out of .
Step 3.1.6.1.3
Factor out of .
Step 3.1.6.1.4
Factor out of .
Step 3.1.6.1.5
Factor out of .
Step 3.1.6.2
Factor by grouping.
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Step 3.1.6.2.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 3.1.6.2.1.1
Factor out of .
Step 3.1.6.2.1.2
Rewrite as plus
Step 3.1.6.2.1.3
Apply the distributive property.
Step 3.1.6.2.2
Factor out the greatest common factor from each group.
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Step 3.1.6.2.2.1
Group the first two terms and the last two terms.
Step 3.1.6.2.2.2
Factor out the greatest common factor (GCF) from each group.
Step 3.1.6.2.3
Factor the polynomial by factoring out the greatest common factor, .
Step 3.1.6.3
Combine exponents.
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Step 3.1.6.3.1
Factor out of .
Step 3.1.6.3.2
Rewrite as .
Step 3.1.6.3.3
Factor out of .
Step 3.1.6.3.4
Rewrite as .
Step 3.1.6.3.5
Raise to the power of .
Step 3.1.6.3.6
Raise to the power of .
Step 3.1.6.3.7
Use the power rule to combine exponents.
Step 3.1.6.3.8
Add and .
Step 3.1.6.3.9
Multiply by .
Step 3.1.7
Rewrite as .
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Step 3.1.7.1
Factor out of .
Step 3.1.7.2
Rewrite as .
Step 3.1.7.3
Move .
Step 3.1.7.4
Rewrite as .
Step 3.1.8
Pull terms out from under the radical.
Step 3.1.9
Rewrite as .
Step 3.1.10
Apply the distributive property.
Step 3.1.11
Multiply by .
Step 3.1.12
Apply the distributive property.
Step 3.2
Multiply by .
Step 4
The final answer is the combination of both solutions.