Calculus Examples

Solve for x x=2 square root of x
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 4
Solve for .
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Factor the left side of the equation.
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Step 4.2.1
Let . Substitute for all occurrences of .
Step 4.2.2
Factor out of .
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Step 4.2.2.1
Factor out of .
Step 4.2.2.2
Factor out of .
Step 4.2.2.3
Factor out of .
Step 4.2.3
Replace all occurrences of with .
Step 4.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.4
Set equal to .
Step 4.5
Set equal to and solve for .
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Step 4.5.1
Set equal to .
Step 4.5.2
Solve for .
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Step 4.5.2.1
Subtract from both sides of the equation.
Step 4.5.2.2
Divide each term in by and simplify.
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Step 4.5.2.2.1
Divide each term in by .
Step 4.5.2.2.2
Simplify the left side.
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Step 4.5.2.2.2.1
Dividing two negative values results in a positive value.
Step 4.5.2.2.2.2
Divide by .
Step 4.5.2.2.3
Simplify the right side.
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Step 4.5.2.2.3.1
Divide by .
Step 4.6
The final solution is all the values that make true.