10c^2-25c-6=0

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Solution for 10c^2-25c-6=0 equation:


Simplifying
10c2 + -25c + -6 = 0

Reorder the terms:
-6 + -25c + 10c2 = 0

Solving
-6 + -25c + 10c2 = 0

Solving for variable 'c'.

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

Divide each side by '10'.
-0.6 + -2.5c + c2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2.5c + 0.6 + c2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2.5c + c2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2.5c + c2 = 0 + 0.6
-2.5c + c2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2.5c + c2 = 0.6

The c term is -2.5c.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5c + 1.5625 + c2 = 0.6 + 1.5625

Reorder the terms:
1.5625 + -2.5c + c2 = 0.6 + 1.5625

Combine like terms: 0.6 + 1.5625 = 2.1625
1.5625 + -2.5c + c2 = 2.1625

Factor a perfect square on the left side:
(c + -1.25)(c + -1.25) = 2.1625

Calculate the square root of the right side: 1.470544117

Break this problem into two subproblems by setting 
(c + -1.25) equal to 1.470544117 and -1.470544117.

Subproblem 1

c + -1.25 = 1.470544117 Simplifying c + -1.25 = 1.470544117 Reorder the terms: -1.25 + c = 1.470544117 Solving -1.25 + c = 1.470544117 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + c = 1.470544117 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + c = 1.470544117 + 1.25 c = 1.470544117 + 1.25 Combine like terms: 1.470544117 + 1.25 = 2.720544117 c = 2.720544117 Simplifying c = 2.720544117

Subproblem 2

c + -1.25 = -1.470544117 Simplifying c + -1.25 = -1.470544117 Reorder the terms: -1.25 + c = -1.470544117 Solving -1.25 + c = -1.470544117 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + c = -1.470544117 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + c = -1.470544117 + 1.25 c = -1.470544117 + 1.25 Combine like terms: -1.470544117 + 1.25 = -0.220544117 c = -0.220544117 Simplifying c = -0.220544117

Solution

The solution to the problem is based on the solutions from the subproblems. c = {2.720544117, -0.220544117}

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