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

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

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

Add 4 and 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