# Solve for c 3 square root of c-2 = square root of 7c+4

3c-2=7c+4
To remove the radical on the left side of the equation, square both sides of the equation.
(3c-2)2=7c+42
Simplify each side of the equation.
Apply the product rule to 3(c-2)12.
32((c-2)12)2=7c+42
Raise 3 to the power of 2.
9((c-2)12)2=7c+42
Multiply the exponents in ((c-2)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
9(c-2)12⋅2=7c+42
Cancel the common factor of 2.
Cancel the common factor.
9(c-2)12⋅2=7c+42
Rewrite the expression.
9(c-2)1=7c+42
9(c-2)1=7c+42
9(c-2)1=7c+42
Simplify.
9(c-2)=7c+42
Apply the distributive property.
9c+9⋅-2=7c+42
Multiply 9 by -2.
9c-18=7c+42
Rewrite 7c+42 as 7c+4.
Use axn=axn to rewrite 7c+4 as (7c+4)12.
9c-18=((7c+4)12)2
Apply the power rule and multiply exponents, (am)n=amn.
9c-18=(7c+4)12⋅2
Combine 12 and 2.
9c-18=(7c+4)22
Cancel the common factor of 2.
Cancel the common factor.
9c-18=(7c+4)22
Divide 1 by 1.
9c-18=(7c+4)1
9c-18=(7c+4)1
Simplify.
9c-18=7c+4
9c-18=7c+4
9c-18=7c+4
Solve for c.
Move all terms containing c to the left side of the equation.
Subtract 7c from both sides of the equation.
9c-18-7c=4
Subtract 7c from 9c.
2c-18=4
2c-18=4
Move all terms not containing c to the right side of the equation.
Add 18 to both sides of the equation.
2c=4+18
2c=22
2c=22
Divide each term by 2 and simplify.
Divide each term in 2c=22 by 2.
2c2=222
Cancel the common factor of 2.
Cancel the common factor.
2c2=222
Divide c by 1.
c=222
c=222
Divide 22 by 2.
c=11
c=11
c=11
Solve for c 3 square root of c-2 = square root of 7c+4

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