3c^2+14c-38=0

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Solution for 3c^2+14c-38=0 equation: 


Simplifying
3c2 + 14c + -38 = 0

Reorder the terms:
-38 + 14c + 3c2 = 0

Solving
-38 + 14c + 3c2 = 0

Solving for variable 'c'.

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

Divide each side by '3'.
-12.66666667 + 4.666666667c + c2 = 0

Move the constant term to the right:

Add '12.66666667' to each side of the equation.
-12.66666667 + 4.666666667c + 12.66666667 + c2 = 0 + 12.66666667

Reorder the terms:
-12.66666667 + 12.66666667 + 4.666666667c + c2 = 0 + 12.66666667

Combine like terms: -12.66666667 + 12.66666667 = 0.00000000
0.00000000 + 4.666666667c + c2 = 0 + 12.66666667
4.666666667c + c2 = 0 + 12.66666667

Combine like terms: 0 + 12.66666667 = 12.66666667
4.666666667c + c2 = 12.66666667

The c term is 4.666666667c.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667c + 5.444444448 + c2 = 12.66666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667c + c2 = 12.66666667 + 5.444444448

Combine like terms: 12.66666667 + 5.444444448 = 18.111111118
5.444444448 + 4.666666667c + c2 = 18.111111118

Factor a perfect square on the left side:
(c + 2.333333334)(c + 2.333333334) = 18.111111118

Calculate the square root of the right side: 4.255715112

Break this problem into two subproblems by setting 
(c + 2.333333334) equal to 4.255715112 and -4.255715112.


Subproblem 1
c + 2.333333334 = 4.255715112

Simplifying
c + 2.333333334 = 4.255715112

Reorder the terms:
2.333333334 + c = 4.255715112

Solving
2.333333334 + c = 4.255715112

Solving for variable 'c'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + c = 4.255715112 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + c = 4.255715112 + -2.333333334
c = 4.255715112 + -2.333333334

Combine like terms: 4.255715112 + -2.333333334 = 1.922381778
c = 1.922381778

Simplifying
c = 1.922381778


Subproblem 2
c + 2.333333334 = -4.255715112

Simplifying
c + 2.333333334 = -4.255715112

Reorder the terms:
2.333333334 + c = -4.255715112

Solving
2.333333334 + c = -4.255715112

Solving for variable 'c'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + c = -4.255715112 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + c = -4.255715112 + -2.333333334
c = -4.255715112 + -2.333333334

Combine like terms: -4.255715112 + -2.333333334 = -6.589048446
c = -6.589048446

Simplifying
c = -6.589048446


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.922381778, -6.589048446}

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