Basic Math Examples

Solve for s (3+4s)/2=2 square root of 1+s
Step 1
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2
To remove the radical on the left side of the equation, square both sides of the equation.
Step 3
Simplify each side of the equation.
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Step 3.1
Use to rewrite as .
Step 3.2
Simplify the left side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Apply the product rule to .
Step 3.2.1.2
Raise to the power of .
Step 3.2.1.3
Multiply the exponents in .
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Step 3.2.1.3.1
Apply the power rule and multiply exponents, .
Step 3.2.1.3.2
Cancel the common factor of .
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Step 3.2.1.3.2.1
Cancel the common factor.
Step 3.2.1.3.2.2
Rewrite the expression.
Step 3.2.1.4
Simplify.
Step 3.2.1.5
Apply the distributive property.
Step 3.2.1.6
Multiply by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Simplify .
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Step 3.3.1.1
Apply the product rule to .
Step 3.3.1.2
Raise to the power of .
Step 4
Solve for .
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Step 4.1
Multiply both sides by .
Step 4.2
Simplify.
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Step 4.2.1
Simplify the left side.
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Step 4.2.1.1
Simplify .
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Step 4.2.1.1.1
Apply the distributive property.
Step 4.2.1.1.2
Simplify the expression.
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Step 4.2.1.1.2.1
Multiply by .
Step 4.2.1.1.2.2
Multiply by .
Step 4.2.1.1.2.3
Reorder and .
Step 4.2.2
Simplify the right side.
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Step 4.2.2.1
Cancel the common factor of .
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Step 4.2.2.1.1
Cancel the common factor.
Step 4.2.2.1.2
Rewrite the expression.
Step 4.3
Solve for .
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Step 4.3.1
Simplify .
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Step 4.3.1.1
Rewrite.
Step 4.3.1.2
Rewrite as .
Step 4.3.1.3
Expand using the FOIL Method.
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Step 4.3.1.3.1
Apply the distributive property.
Step 4.3.1.3.2
Apply the distributive property.
Step 4.3.1.3.3
Apply the distributive property.
Step 4.3.1.4
Simplify and combine like terms.
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Step 4.3.1.4.1
Simplify each term.
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Step 4.3.1.4.1.1
Multiply by .
Step 4.3.1.4.1.2
Multiply by .
Step 4.3.1.4.1.3
Multiply by .
Step 4.3.1.4.1.4
Rewrite using the commutative property of multiplication.
Step 4.3.1.4.1.5
Multiply by by adding the exponents.
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Step 4.3.1.4.1.5.1
Move .
Step 4.3.1.4.1.5.2
Multiply by .
Step 4.3.1.4.1.6
Multiply by .
Step 4.3.1.4.2
Add and .
Step 4.3.2
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.3.3
Move all terms containing to the left side of the equation.
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Step 4.3.3.1
Subtract from both sides of the equation.
Step 4.3.3.2
Subtract from .
Step 4.3.4
Move all terms to the left side of the equation and simplify.
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Step 4.3.4.1
Subtract from both sides of the equation.
Step 4.3.4.2
Subtract from .
Step 4.3.5
Use the quadratic formula to find the solutions.
Step 4.3.6
Substitute the values , , and into the quadratic formula and solve for .
Step 4.3.7
Simplify.
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Step 4.3.7.1
Simplify the numerator.
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Step 4.3.7.1.1
Raise to the power of .
Step 4.3.7.1.2
Multiply .
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Step 4.3.7.1.2.1
Multiply by .
Step 4.3.7.1.2.2
Multiply by .
Step 4.3.7.1.3
Add and .
Step 4.3.7.1.4
Rewrite as .
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Step 4.3.7.1.4.1
Factor out of .
Step 4.3.7.1.4.2
Rewrite as .
Step 4.3.7.1.5
Pull terms out from under the radical.
Step 4.3.7.2
Multiply by .
Step 4.3.7.3
Simplify .
Step 4.3.8
The final answer is the combination of both solutions.
Step 5
Exclude the solutions that do not make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: