Basic Math Examples

Solve for a square root of a+6 = square root of 2a-1
Step 1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2
Simplify each side of the equation.
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Step 2.1
Use to rewrite as .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Multiply the exponents in .
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Step 2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.2.1.1.2
Cancel the common factor of .
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Step 2.2.1.1.2.1
Cancel the common factor.
Step 2.2.1.1.2.2
Rewrite the expression.
Step 2.2.1.2
Simplify.
Step 2.3
Simplify the right side.
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Step 2.3.1
Simplify .
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Step 2.3.1.1
Rewrite as .
Step 2.3.1.2
Expand using the FOIL Method.
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Step 2.3.1.2.1
Apply the distributive property.
Step 2.3.1.2.2
Apply the distributive property.
Step 2.3.1.2.3
Apply the distributive property.
Step 2.3.1.3
Simplify and combine like terms.
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Step 2.3.1.3.1
Simplify each term.
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Step 2.3.1.3.1.1
Multiply .
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Step 2.3.1.3.1.1.1
Raise to the power of .
Step 2.3.1.3.1.1.2
Raise to the power of .
Step 2.3.1.3.1.1.3
Use the power rule to combine exponents.
Step 2.3.1.3.1.1.4
Add and .
Step 2.3.1.3.1.2
Rewrite as .
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Step 2.3.1.3.1.2.1
Use to rewrite as .
Step 2.3.1.3.1.2.2
Apply the power rule and multiply exponents, .
Step 2.3.1.3.1.2.3
Combine and .
Step 2.3.1.3.1.2.4
Cancel the common factor of .
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Step 2.3.1.3.1.2.4.1
Cancel the common factor.
Step 2.3.1.3.1.2.4.2
Rewrite the expression.
Step 2.3.1.3.1.2.5
Simplify.
Step 2.3.1.3.1.3
Move to the left of .
Step 2.3.1.3.1.4
Rewrite as .
Step 2.3.1.3.1.5
Rewrite as .
Step 2.3.1.3.1.6
Multiply by .
Step 2.3.1.3.2
Subtract from .
Step 3
Solve for .
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Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right side of the equation.
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Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from both sides of the equation.
Step 3.2.3
Subtract from .
Step 3.2.4
Subtract from .
Step 4
To remove the radical on the left side of the equation, square both sides of the equation.
Step 5
Simplify each side of the equation.
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Step 5.1
Use to rewrite as .
Step 5.2
Simplify the left side.
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Step 5.2.1
Simplify .
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Step 5.2.1.1
Apply the product rule to .
Step 5.2.1.2
Multiply .
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Step 5.2.1.2.1
Factor out negative.
Step 5.2.1.2.2
Raise to the power of .
Step 5.2.1.2.3
Use the power rule to combine exponents.
Step 5.2.1.2.4
Write as a fraction with a common denominator.
Step 5.2.1.2.5
Combine the numerators over the common denominator.
Step 5.2.1.2.6
Add and .
Step 5.2.1.3
Use the power rule to distribute the exponent.
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Step 5.2.1.3.1
Apply the product rule to .
Step 5.2.1.3.2
Apply the product rule to .
Step 5.2.1.4
Raise to the power of .
Step 5.2.1.5
Multiply by .
Step 5.2.1.6
Multiply the exponents in .
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Step 5.2.1.6.1
Apply the power rule and multiply exponents, .
Step 5.2.1.6.2
Cancel the common factor of .
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Step 5.2.1.6.2.1
Cancel the common factor.
Step 5.2.1.6.2.2
Rewrite the expression.
Step 5.2.1.7
Raise to the power of .
Step 5.2.1.8
Multiply the exponents in .
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Step 5.2.1.8.1
Apply the power rule and multiply exponents, .
Step 5.2.1.8.2
Cancel the common factor of .
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Step 5.2.1.8.2.1
Cancel the common factor.
Step 5.2.1.8.2.2
Rewrite the expression.
Step 5.2.1.9
Simplify.
Step 5.3
Simplify the right side.
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Step 5.3.1
Simplify .
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Step 5.3.1.1
Rewrite as .
Step 5.3.1.2
Expand using the FOIL Method.
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Step 5.3.1.2.1
Apply the distributive property.
Step 5.3.1.2.2
Apply the distributive property.
Step 5.3.1.2.3
Apply the distributive property.
Step 5.3.1.3
Simplify and combine like terms.
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Step 5.3.1.3.1
Simplify each term.
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Step 5.3.1.3.1.1
Rewrite using the commutative property of multiplication.
Step 5.3.1.3.1.2
Multiply by by adding the exponents.
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Step 5.3.1.3.1.2.1
Move .
Step 5.3.1.3.1.2.2
Multiply by .
Step 5.3.1.3.1.3
Multiply by .
Step 5.3.1.3.1.4
Multiply by .
Step 5.3.1.3.1.5
Multiply by .
Step 5.3.1.3.1.6
Multiply by .
Step 5.3.1.3.1.7
Multiply by .
Step 5.3.1.3.2
Subtract from .
Step 6
Solve for .
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Step 6.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 6.2
Move all terms containing to the left side of the equation.
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Step 6.2.1
Subtract from both sides of the equation.
Step 6.2.2
Subtract from .
Step 6.3
Use the quadratic formula to find the solutions.
Step 6.4
Substitute the values , , and into the quadratic formula and solve for .
Step 6.5
Simplify.
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Step 6.5.1
Simplify the numerator.
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Step 6.5.1.1
Raise to the power of .
Step 6.5.1.2
Multiply .
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Step 6.5.1.2.1
Multiply by .
Step 6.5.1.2.2
Multiply by .
Step 6.5.1.3
Subtract from .
Step 6.5.1.4
Rewrite as .
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Step 6.5.1.4.1
Factor out of .
Step 6.5.1.4.2
Rewrite as .
Step 6.5.1.5
Pull terms out from under the radical.
Step 6.5.2
Multiply by .
Step 6.5.3
Simplify .
Step 6.6
The final answer is the combination of both solutions.
Step 7
Exclude the solutions that do not make true.
Step 8
The result can be shown in multiple forms.
Exact Form:
Decimal Form: