Solve for c square root of 76-2c = square root of c/9

Math
76-2c=c9
To remove the radical on the left side of the equation, square both sides of the equation.
76-2c2=c92
Simplify each side of the equation.
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Multiply the exponents in ((76-2c)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(76-2c)12⋅2=c92
Cancel the common factor of 2.
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Cancel the common factor.
(76-2c)12⋅2=c92
Rewrite the expression.
(76-2c)1=c92
(76-2c)1=c92
(76-2c)1=c92
Simplify.
76-2c=c92
Rewrite c9 as (13)2c.
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Factor the perfect power 12 out of c.
76-2c=12c92
Factor the perfect power 32 out of 9.
76-2c=12c32⋅12
Rearrange the fraction 12c32⋅1.
76-2c=(13)2c2
76-2c=(13)2c2
Pull terms out from under the radical.
76-2c=(13c)2
Combine 13 and c.
76-2c=(c3)2
Apply the product rule to c3.
76-2c=c232
Rewrite c2 as c.
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Use axn=axn to rewrite c as c12.
76-2c=(c12)232
Apply the power rule and multiply exponents, (am)n=amn.
76-2c=c12⋅232
Combine 12 and 2.
76-2c=c2232
Cancel the common factor of 2.
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Cancel the common factor.
76-2c=c2232
Divide 1 by 1.
76-2c=c132
76-2c=c132
Simplify.
76-2c=c32
76-2c=c32
Raise 3 to the power of 2.
76-2c=c9
76-2c=c9
Solve for c.
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Move all terms containing c to the left side of the equation.
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Subtract c9 from both sides of the equation.
76-2c-c9=0
To write -2c as a fraction with a common denominator, multiply by 99.
76-2c⋅99-c9=0
Combine -2c and 99.
76+-2c⋅99-c9=0
Combine the numerators over the common denominator.
76+-2c⋅9-c9=0
Simplify each term.
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Simplify the numerator.
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Factor c out of -2c⋅9-c.
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Factor c out of -2c⋅9.
76+c(-2⋅9)-c9=0
Factor c out of -c.
76+c(-2⋅9)+c⋅-19=0
Factor c out of c(-2⋅9)+c⋅-1.
76+c(-2⋅9-1)9=0
76+c(-2⋅9-1)9=0
Multiply -2 by 9.
76+c(-18-1)9=0
Subtract 1 from -18.
76+c⋅-199=0
76+c⋅-199=0
Move -19 to the left of c.
76+-19⋅c9=0
Move the negative in front of the fraction.
76-19c9=0
76-19c9=0
76-19c9=0
Subtract 76 from both sides of the equation.
-19c9=-76
Multiply both sides of the equation by -919.
-919⋅(-19c9)=-919⋅-76
Simplify both sides of the equation.
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Simplify -919⋅(-19c9).
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Cancel the common factor of 9.
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Move the leading negative in -919 into the numerator.
-919⋅(-19c9)=-919⋅-76
Move the leading negative in -19c9 into the numerator.
-919⋅-19c9=-919⋅-76
Factor 9 out of -9.
9(-1)19⋅-19c9=-919⋅-76
Cancel the common factor.
9⋅-119⋅-19c9=-919⋅-76
Rewrite the expression.
-119⋅(-19c)=-919⋅-76
-119⋅(-19c)=-919⋅-76
Cancel the common factor of 19.
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Factor 19 out of -19c.
-119⋅(19(-c))=-919⋅-76
Cancel the common factor.
-119⋅(19(-c))=-919⋅-76
Rewrite the expression.
-1⋅(-c)=-919⋅-76
-1⋅(-c)=-919⋅-76
Multiply.
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Multiply -1 by -1.
1⋅c=-919⋅-76
Multiply c by 1.
c=-919⋅-76
c=-919⋅-76
c=-919⋅-76
Simplify -919⋅-76.
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Cancel the common factor of 19.
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Move the leading negative in -919 into the numerator.
c=-919⋅-76
Factor 19 out of -76.
c=-919⋅(19(-4))
Cancel the common factor.
c=-919⋅(19⋅-4)
Rewrite the expression.
c=-9⋅-4
c=-9⋅-4
Multiply -9 by -4.
c=36
c=36
c=36
c=36
Solve for c square root of 76-2c = square root of c/9
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