Basic Math Examples

Solve for a b^2+6b+a=(b+a)^2
Step 1
Simplify .
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Step 1.1
Rewrite.
Step 1.2
Rewrite as .
Step 1.3
Expand using the FOIL Method.
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Step 1.3.1
Apply the distributive property.
Step 1.3.2
Apply the distributive property.
Step 1.3.3
Apply the distributive property.
Step 1.4
Simplify and combine like terms.
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Step 1.4.1
Simplify each term.
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Step 1.4.1.1
Multiply by .
Step 1.4.1.2
Multiply by .
Step 1.4.2
Add and .
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Step 1.4.2.1
Reorder and .
Step 1.4.2.2
Add and .
Step 2
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 3
Subtract from both sides of the equation.
Step 4
Move all terms to the left side of the equation and simplify.
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Step 4.1
Move all the expressions to the left side of the equation.
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Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Subtract from both sides of the equation.
Step 4.2
Combine the opposite terms in .
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Step 4.2.1
Subtract from .
Step 4.2.2
Add and .
Step 5
Use the quadratic formula to find the solutions.
Step 6
Substitute the values , , and into the quadratic formula and solve for .
Step 7
Simplify.
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Step 7.1
Simplify the numerator.
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Step 7.1.1
Apply the distributive property.
Step 7.1.2
Multiply by .
Step 7.1.3
Multiply by .
Step 7.1.4
Rewrite as .
Step 7.1.5
Expand using the FOIL Method.
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Step 7.1.5.1
Apply the distributive property.
Step 7.1.5.2
Apply the distributive property.
Step 7.1.5.3
Apply the distributive property.
Step 7.1.6
Simplify and combine like terms.
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Step 7.1.6.1
Simplify each term.
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Step 7.1.6.1.1
Rewrite using the commutative property of multiplication.
Step 7.1.6.1.2
Multiply by by adding the exponents.
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Step 7.1.6.1.2.1
Move .
Step 7.1.6.1.2.2
Multiply by .
Step 7.1.6.1.3
Multiply by .
Step 7.1.6.1.4
Multiply by .
Step 7.1.6.1.5
Multiply by .
Step 7.1.6.1.6
Multiply by .
Step 7.1.6.2
Subtract from .
Step 7.1.7
Multiply .
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Step 7.1.7.1
Multiply by .
Step 7.1.7.2
Multiply by .
Step 7.1.8
Add and .
Step 7.2
Multiply by .
Step 8
The final answer is the combination of both solutions.