c^2-14c+2=0

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Solution for c^2-14c+2=0 equation:


Simplifying
c2 + -14c + 2 = 0

Reorder the terms:
2 + -14c + c2 = 0

Solving
2 + -14c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -14c + -2 + c2 = 0 + -2

Reorder the terms:
2 + -2 + -14c + c2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -14c + c2 = 0 + -2
-14c + c2 = 0 + -2

Combine like terms: 0 + -2 = -2
-14c + c2 = -2

The c term is -14c.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14c + 49 + c2 = -2 + 49

Reorder the terms:
49 + -14c + c2 = -2 + 49

Combine like terms: -2 + 49 = 47
49 + -14c + c2 = 47

Factor a perfect square on the left side:
(c + -7)(c + -7) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(c + -7) equal to 6.8556546 and -6.8556546.

Subproblem 1

c + -7 = 6.8556546 Simplifying c + -7 = 6.8556546 Reorder the terms: -7 + c = 6.8556546 Solving -7 + c = 6.8556546 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + c = 6.8556546 + 7 Combine like terms: -7 + 7 = 0 0 + c = 6.8556546 + 7 c = 6.8556546 + 7 Combine like terms: 6.8556546 + 7 = 13.8556546 c = 13.8556546 Simplifying c = 13.8556546

Subproblem 2

c + -7 = -6.8556546 Simplifying c + -7 = -6.8556546 Reorder the terms: -7 + c = -6.8556546 Solving -7 + c = -6.8556546 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + c = -6.8556546 + 7 Combine like terms: -7 + 7 = 0 0 + c = -6.8556546 + 7 c = -6.8556546 + 7 Combine like terms: -6.8556546 + 7 = 0.1443454 c = 0.1443454 Simplifying c = 0.1443454

Solution

The solution to the problem is based on the solutions from the subproblems. c = {13.8556546, 0.1443454}

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