Finite Math Examples

Solve Using the Quadratic Formula (2m+4)^2+(3m)^2=(5m)^2
Step 1
Move all terms to the left side of the equation and simplify.
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Step 1.1
Simplify the left side.
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Step 1.1.1
Simplify each term.
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Step 1.1.1.1
Apply the product rule to .
Step 1.1.1.2
Raise to the power of .
Step 1.2
Simplify the right side.
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Step 1.2.1
Simplify .
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Step 1.2.1.1
Apply the product rule to .
Step 1.2.1.2
Raise to the power of .
Step 1.3
Subtract from both sides of the equation.
Step 1.4
Simplify .
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Step 1.4.1
Simplify each term.
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Step 1.4.1.1
Rewrite as .
Step 1.4.1.2
Expand using the FOIL Method.
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Step 1.4.1.2.1
Apply the distributive property.
Step 1.4.1.2.2
Apply the distributive property.
Step 1.4.1.2.3
Apply the distributive property.
Step 1.4.1.3
Simplify and combine like terms.
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Step 1.4.1.3.1
Simplify each term.
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Step 1.4.1.3.1.1
Rewrite using the commutative property of multiplication.
Step 1.4.1.3.1.2
Multiply by by adding the exponents.
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Step 1.4.1.3.1.2.1
Move .
Step 1.4.1.3.1.2.2
Multiply by .
Step 1.4.1.3.1.3
Multiply by .
Step 1.4.1.3.1.4
Multiply by .
Step 1.4.1.3.1.5
Multiply by .
Step 1.4.1.3.1.6
Multiply by .
Step 1.4.1.3.2
Add and .
Step 1.4.2
Add and .
Step 1.4.3
Subtract from .
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 .
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Step 4.1.2.1
Multiply by .
Step 4.1.2.2
Multiply by .
Step 4.1.3
Add and .
Step 4.1.4
Rewrite as .
Step 4.1.5
Pull terms out from under the radical, assuming positive real numbers.
Step 4.2
Multiply by .
Step 4.3
Simplify .
Step 5
The final answer is the combination of both solutions.