Basic Math Examples

Solve for y x^2+y^2+4x-10y=7
Step 1
Subtract from both sides of the equation.
Step 2
Use the quadratic formula to find the solutions.
Step 3
Substitute the values , , and into the quadratic formula and solve for .
Step 4
Simplify.
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Step 4.1
Simplify the numerator.
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Step 4.1.1
Raise to the power of .
Step 4.1.2
Multiply by .
Step 4.1.3
Apply the distributive property.
Step 4.1.4
Simplify.
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Step 4.1.4.1
Multiply by .
Step 4.1.4.2
Multiply by .
Step 4.1.5
Add and .
Step 4.1.6
Rewrite in a factored form.
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Step 4.1.6.1
Factor out of .
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Step 4.1.6.1.1
Factor out of .
Step 4.1.6.1.2
Factor out of .
Step 4.1.6.1.3
Factor out of .
Step 4.1.6.1.4
Factor out of .
Step 4.1.6.1.5
Factor out of .
Step 4.1.6.2
Factor by grouping.
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Step 4.1.6.2.1
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 4.1.6.2.1.1
Factor out of .
Step 4.1.6.2.1.2
Rewrite as plus
Step 4.1.6.2.1.3
Apply the distributive property.
Step 4.1.6.2.2
Factor out the greatest common factor from each group.
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Step 4.1.6.2.2.1
Group the first two terms and the last two terms.
Step 4.1.6.2.2.2
Factor out the greatest common factor (GCF) from each group.
Step 4.1.6.2.3
Factor the polynomial by factoring out the greatest common factor, .
Step 4.1.7
Rewrite as .
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Step 4.1.7.1
Rewrite as .
Step 4.1.7.2
Rewrite as .
Step 4.1.7.3
Add parentheses.
Step 4.1.8
Pull terms out from under the radical.
Step 4.1.9
Raise to the power of .
Step 4.2
Multiply by .
Step 4.3
Simplify .
Step 5
The final answer is the combination of both solutions.