c^2-28c-30=0

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Solution for c^2-28c-30=0 equation: 


Simplifying
c2 + -28c + -30 = 0

Reorder the terms:
-30 + -28c + c2 = 0

Solving
-30 + -28c + c2 = 0

Solving for variable 'c'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -28c + 30 + c2 = 0 + 30

Reorder the terms:
-30 + 30 + -28c + c2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -28c + c2 = 0 + 30
-28c + c2 = 0 + 30

Combine like terms: 0 + 30 = 30
-28c + c2 = 30

The c term is -28c.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28c + 196 + c2 = 30 + 196

Reorder the terms:
196 + -28c + c2 = 30 + 196

Combine like terms: 30 + 196 = 226
196 + -28c + c2 = 226

Factor a perfect square on the left side:
(c + -14)(c + -14) = 226

Calculate the square root of the right side: 15.033296378

Break this problem into two subproblems by setting 
(c + -14) equal to 15.033296378 and -15.033296378.


Subproblem 1
c + -14 = 15.033296378

Simplifying
c + -14 = 15.033296378

Reorder the terms:
-14 + c = 15.033296378

Solving
-14 + c = 15.033296378

Solving for variable 'c'.

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

Add '14' to each side of the equation.
-14 + 14 + c = 15.033296378 + 14

Combine like terms: -14 + 14 = 0
0 + c = 15.033296378 + 14
c = 15.033296378 + 14

Combine like terms: 15.033296378 + 14 = 29.033296378
c = 29.033296378

Simplifying
c = 29.033296378


Subproblem 2
c + -14 = -15.033296378

Simplifying
c + -14 = -15.033296378

Reorder the terms:
-14 + c = -15.033296378

Solving
-14 + c = -15.033296378

Solving for variable 'c'.

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

Add '14' to each side of the equation.
-14 + 14 + c = -15.033296378 + 14

Combine like terms: -14 + 14 = 0
0 + c = -15.033296378 + 14
c = -15.033296378 + 14

Combine like terms: -15.033296378 + 14 = -1.033296378
c = -1.033296378

Simplifying
c = -1.033296378


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {29.033296378, -1.033296378}

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