2c^2-16c-30=0

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Solution for 2c^2-16c-30=0 equation:


Simplifying
2c2 + -16c + -30 = 0

Reorder the terms:
-30 + -16c + 2c2 = 0

Solving
-30 + -16c + 2c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -8c + c2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + -8c + c2)' equal to zero and attempt to solve:

Simplifying
-15 + -8c + c2 = 0

Solving
-15 + -8c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -8c + 15 + c2 = 0 + 15

Reorder the terms:
-15 + 15 + -8c + c2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -8c + c2 = 0 + 15
-8c + c2 = 0 + 15

Combine like terms: 0 + 15 = 15
-8c + c2 = 15

The c term is -8c.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8c + 16 + c2 = 15 + 16

Reorder the terms:
16 + -8c + c2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + -8c + c2 = 31

Factor a perfect square on the left side:
(c + -4)(c + -4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(c + -4) equal to 5.567764363 and -5.567764363.


Subproblem 1
c + -4 = 5.567764363

Simplifying
c + -4 = 5.567764363

Reorder the terms:
-4 + c = 5.567764363

Solving
-4 + c = 5.567764363

Solving for variable 'c'.

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

Add '4' to each side of the equation.
-4 + 4 + c = 5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + c = 5.567764363 + 4
c = 5.567764363 + 4

Combine like terms: 5.567764363 + 4 = 9.567764363
c = 9.567764363

Simplifying
c = 9.567764363


Subproblem 2
c + -4 = -5.567764363

Simplifying
c + -4 = -5.567764363

Reorder the terms:
-4 + c = -5.567764363

Solving
-4 + c = -5.567764363

Solving for variable 'c'.

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

Add '4' to each side of the equation.
-4 + 4 + c = -5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + c = -5.567764363 + 4
c = -5.567764363 + 4

Combine like terms: -5.567764363 + 4 = -1.567764363
c = -1.567764363

Simplifying
c = -1.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {9.567764363, -1.567764363}
Solution
c = {9.567764363, -1.567764363}

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