Basic Math Examples

Solve for t (4t^2)/5=(9t)/5+11/10
Step 1
Multiply both sides by .
Step 2
Simplify.
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Step 2.1
Simplify the left side.
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Step 2.1.1
Cancel the common factor of .
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Step 2.1.1.1
Cancel the common factor.
Step 2.1.1.2
Rewrite the expression.
Step 2.2
Simplify the right side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
Cancel the common factor of .
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Step 2.2.1.2.1
Cancel the common factor.
Step 2.2.1.2.2
Rewrite the expression.
Step 2.2.1.3
Cancel the common factor of .
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Step 2.2.1.3.1
Factor out of .
Step 2.2.1.3.2
Cancel the common factor.
Step 2.2.1.3.3
Rewrite the expression.
Step 3
Solve for .
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Multiply through by the least common denominator , then simplify.
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Step 3.3.1
Apply the distributive property.
Step 3.3.2
Simplify.
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Step 3.3.2.1
Multiply by .
Step 3.3.2.2
Multiply by .
Step 3.3.2.3
Cancel the common factor of .
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Step 3.3.2.3.1
Move the leading negative in into the numerator.
Step 3.3.2.3.2
Cancel the common factor.
Step 3.3.2.3.3
Rewrite the expression.
Step 3.4
Use the quadratic formula to find the solutions.
Step 3.5
Substitute the values , , and into the quadratic formula and solve for .
Step 3.6
Simplify.
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Step 3.6.1
Simplify the numerator.
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Step 3.6.1.1
Raise to the power of .
Step 3.6.1.2
Multiply .
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Step 3.6.1.2.1
Multiply by .
Step 3.6.1.2.2
Multiply by .
Step 3.6.1.3
Add and .
Step 3.6.1.4
Rewrite as .
Step 3.6.1.5
Pull terms out from under the radical, assuming positive real numbers.
Step 3.6.2
Multiply by .
Step 3.6.3
Simplify .
Step 3.7
The final answer is the combination of both solutions.
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: