Basic Math Examples

Solve for t 0.5=(6t)/(t^2+4)
Step 1
Rewrite the equation as .
Step 2
Find the LCD of the terms in the equation.
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Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
Remove parentheses.
Step 2.3
The LCM of one and any expression is the expression.
Step 3
Multiply each term in by to eliminate the fractions.
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Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Rewrite the expression.
Step 3.3
Simplify the right side.
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Step 3.3.1
Apply the distributive property.
Step 3.3.2
Multiply by .
Step 4
Solve the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Factor out of .
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Step 4.3.1
Reorder and .
Step 4.3.2
Factor out of .
Step 4.3.3
Factor out of .
Step 4.3.4
Factor out of .
Step 4.3.5
Factor out of .
Step 4.3.6
Factor out of .
Step 4.4
Divide each term in by and simplify.
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Step 4.4.1
Divide each term in by .
Step 4.4.2
Simplify the left side.
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Step 4.4.2.1
Cancel the common factor of .
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Step 4.4.2.1.1
Cancel the common factor.
Step 4.4.2.1.2
Divide by .
Step 4.4.3
Simplify the right side.
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Step 4.4.3.1
Divide by .
Step 4.5
Use the quadratic formula to find the solutions.
Step 4.6
Substitute the values , , and into the quadratic formula and solve for .
Step 4.7
Simplify.
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Step 4.7.1
Simplify the numerator.
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Step 4.7.1.1
Raise to the power of .
Step 4.7.1.2
Multiply .
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Step 4.7.1.2.1
Multiply by .
Step 4.7.1.2.2
Multiply by .
Step 4.7.1.3
Subtract from .
Step 4.7.1.4
Rewrite as .
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Step 4.7.1.4.1
Factor out of .
Step 4.7.1.4.2
Rewrite as .
Step 4.7.1.5
Pull terms out from under the radical.
Step 4.7.2
Multiply by .
Step 4.7.3
Simplify .
Step 4.8
The final answer is the combination of both solutions.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: