7c(c-2)=34

Solution for 7c(c-2)=34 equation:

Simplifying
7c(c + -2) = 34

Reorder the terms:
7c(-2 + c) = 34
(-2 * 7c + c * 7c) = 34
(-14c + 7c2) = 34

Solving
-14c + 7c2 = 34

Solving for variable 'c'.

Reorder the terms:
-34 + -14c + 7c2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + -14c + 7c2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-4.857142857 + -2c + c2 = 0

Move the constant term to the right:

Add '4.857142857' to each side of the equation.
-4.857142857 + -2c + 4.857142857 + c2 = 0 + 4.857142857

Reorder the terms:
-4.857142857 + 4.857142857 + -2c + c2 = 0 + 4.857142857

Combine like terms: -4.857142857 + 4.857142857 = 0.000000000
0.000000000 + -2c + c2 = 0 + 4.857142857
-2c + c2 = 0 + 4.857142857

Combine like terms: 0 + 4.857142857 = 4.857142857
-2c + c2 = 4.857142857

The c term is -2c.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2c + 1 + c2 = 4.857142857 + 1

Reorder the terms:
1 + -2c + c2 = 4.857142857 + 1

Combine like terms: 4.857142857 + 1 = 5.857142857
1 + -2c + c2 = 5.857142857

Factor a perfect square on the left side:
(c + -1)(c + -1) = 5.857142857

Calculate the square root of the right side: 2.420153478

Break this problem into two subproblems by setting 
(c + -1) equal to 2.420153478 and -2.420153478.

Subproblem 1
c + -1 = 2.420153478

Simplifying
c + -1 = 2.420153478

Reorder the terms:
-1 + c = 2.420153478

Solving
-1 + c = 2.420153478

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + c = 2.420153478 + 1

Combine like terms: -1 + 1 = 0
0 + c = 2.420153478 + 1
c = 2.420153478 + 1

Combine like terms: 2.420153478 + 1 = 3.420153478
c = 3.420153478

Simplifying
c = 3.420153478

Subproblem 2
c + -1 = -2.420153478

Simplifying
c + -1 = -2.420153478

Reorder the terms:
-1 + c = -2.420153478

Solving
-1 + c = -2.420153478

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + c = -2.420153478 + 1

Combine like terms: -1 + 1 = 0
0 + c = -2.420153478 + 1
c = -2.420153478 + 1

Combine like terms: -2.420153478 + 1 = -1.420153478
c = -1.420153478

Simplifying
c = -1.420153478

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.420153478, -1.420153478}