-2c^2-14c+5=0

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Solution for -2c^2-14c+5=0 equation:


Simplifying
-2c2 + -14c + 5 = 0

Reorder the terms:
5 + -14c + -2c2 = 0

Solving
5 + -14c + -2c2 = 0

Solving for variable 'c'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-2.5 + 7c + c2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 7c + 2.5 + c2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 7c + c2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 7c + c2 = 0 + 2.5
7c + c2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
7c + c2 = 2.5

The c term is 7c.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7c + 12.25 + c2 = 2.5 + 12.25

Reorder the terms:
12.25 + 7c + c2 = 2.5 + 12.25

Combine like terms: 2.5 + 12.25 = 14.75
12.25 + 7c + c2 = 14.75

Factor a perfect square on the left side:
(c + 3.5)(c + 3.5) = 14.75

Calculate the square root of the right side: 3.840572874

Break this problem into two subproblems by setting 
(c + 3.5) equal to 3.840572874 and -3.840572874.

Subproblem 1

c + 3.5 = 3.840572874 Simplifying c + 3.5 = 3.840572874 Reorder the terms: 3.5 + c = 3.840572874 Solving 3.5 + c = 3.840572874 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = 3.840572874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = 3.840572874 + -3.5 c = 3.840572874 + -3.5 Combine like terms: 3.840572874 + -3.5 = 0.340572874 c = 0.340572874 Simplifying c = 0.340572874

Subproblem 2

c + 3.5 = -3.840572874 Simplifying c + 3.5 = -3.840572874 Reorder the terms: 3.5 + c = -3.840572874 Solving 3.5 + c = -3.840572874 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = -3.840572874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = -3.840572874 + -3.5 c = -3.840572874 + -3.5 Combine like terms: -3.840572874 + -3.5 = -7.340572874 c = -7.340572874 Simplifying c = -7.340572874

Solution

The solution to the problem is based on the solutions from the subproblems. c = {0.340572874, -7.340572874}

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