Finite Math Examples

Solve by Completing the Square 2x^2+4x-3=0
Step 1
Add to both sides of the equation.
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify each term.
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Step 2.2.1.1
Cancel the common factor of .
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Step 2.2.1.1.1
Cancel the common factor.
Step 2.2.1.1.2
Divide by .
Step 2.2.1.2
Cancel the common factor of and .
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Step 2.2.1.2.1
Factor out of .
Step 2.2.1.2.2
Cancel the common factors.
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Step 2.2.1.2.2.1
Factor out of .
Step 2.2.1.2.2.2
Cancel the common factor.
Step 2.2.1.2.2.3
Rewrite the expression.
Step 2.2.1.2.2.4
Divide by .
Step 3
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of .
Step 4
Add the term to each side of the equation.
Step 5
Simplify the equation.
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Step 5.1
Simplify the left side.
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Step 5.1.1
One to any power is one.
Step 5.2
Simplify the right side.
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Step 5.2.1
Simplify .
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Step 5.2.1.1
One to any power is one.
Step 5.2.1.2
Write as a fraction with a common denominator.
Step 5.2.1.3
Combine the numerators over the common denominator.
Step 5.2.1.4
Add and .
Step 6
Factor the perfect trinomial square into .
Step 7
Solve the equation for .
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Step 7.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 7.2
Simplify .
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Step 7.2.1
Rewrite as .
Step 7.2.2
Multiply by .
Step 7.2.3
Combine and simplify the denominator.
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Step 7.2.3.1
Multiply by .
Step 7.2.3.2
Raise to the power of .
Step 7.2.3.3
Raise to the power of .
Step 7.2.3.4
Use the power rule to combine exponents.
Step 7.2.3.5
Add and .
Step 7.2.3.6
Rewrite as .
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Step 7.2.3.6.1
Use to rewrite as .
Step 7.2.3.6.2
Apply the power rule and multiply exponents, .
Step 7.2.3.6.3
Combine and .
Step 7.2.3.6.4
Cancel the common factor of .
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Step 7.2.3.6.4.1
Cancel the common factor.
Step 7.2.3.6.4.2
Rewrite the expression.
Step 7.2.3.6.5
Evaluate the exponent.
Step 7.2.4
Simplify the numerator.
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Step 7.2.4.1
Combine using the product rule for radicals.
Step 7.2.4.2
Multiply by .
Step 7.3
Subtract from both sides of the equation.
Step 8
The result can be shown in multiple forms.
Exact Form:
Decimal Form: