Solve for a square root of a+6 = square root of 2a-1

Math
a+6=2a-1
To remove the radical on the left side of the equation, square both sides of the equation.
a+62=2a-12
Simplify each side of the equation.
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Multiply the exponents in ((a+6)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(a+6)12⋅2=2a-12
Cancel the common factor of 2.
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Cancel the common factor.
(a+6)12⋅2=2a-12
Rewrite the expression.
(a+6)1=2a-12
(a+6)1=2a-12
(a+6)1=2a-12
Simplify.
a+6=2a-12
Rewrite 2a-12 as 2a-1.
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Use axn=axn to rewrite 2a-1 as (2a-1)12.
a+6=((2a-1)12)2
Apply the power rule and multiply exponents, (am)n=amn.
a+6=(2a-1)12⋅2
Combine 12 and 2.
a+6=(2a-1)22
Cancel the common factor of 2.
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Cancel the common factor.
a+6=(2a-1)22
Divide 1 by 1.
a+6=(2a-1)1
a+6=(2a-1)1
Simplify.
a+6=2a-1
a+6=2a-1
a+6=2a-1
Solve for a.
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Move all terms containing a to the left side of the equation.
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Subtract 2a from both sides of the equation.
a+6-2a=-1
Subtract 2a from a.
-a+6=-1
-a+6=-1
Move all terms not containing a to the right side of the equation.
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Subtract 6 from both sides of the equation.
-a=-1-6
Subtract 6 from -1.
-a=-7
-a=-7
Multiply each term in -a=-7 by -1
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Multiply each term in -a=-7 by -1.
(-a)⋅-1=(-7)⋅-1
Multiply (-a)⋅-1.
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Multiply -1 by -1.
1a=(-7)⋅-1
Multiply a by 1.
a=(-7)⋅-1
a=(-7)⋅-1
Multiply -7 by -1.
a=7
a=7
a=7
Solve for a square root of a+6 = square root of 2a-1

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