(-5-2c)(-6c)+7=

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Solution for (-5-2c)(-6c)+7= equation:


Simplifying
(-5 + -2c)(-6c) + 7 = 0

Remove parenthesis around (-6c)
(-5 + -2c) * -6c + 7 = 0

Reorder the terms for easier multiplication:
-6c(-5 + -2c) + 7 = 0
(-5 * -6c + -2c * -6c) + 7 = 0
(30c + 12c2) + 7 = 0

Reorder the terms:
7 + 30c + 12c2 = 0

Solving
7 + 30c + 12c2 = 0

Solving for variable 'c'.

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

Divide each side by '12'.
0.5833333333 + 2.5c + c2 = 0

Move the constant term to the right:

Add '-0.5833333333' to each side of the equation.
0.5833333333 + 2.5c + -0.5833333333 + c2 = 0 + -0.5833333333

Reorder the terms:
0.5833333333 + -0.5833333333 + 2.5c + c2 = 0 + -0.5833333333

Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000
0.0000000000 + 2.5c + c2 = 0 + -0.5833333333
2.5c + c2 = 0 + -0.5833333333

Combine like terms: 0 + -0.5833333333 = -0.5833333333
2.5c + c2 = -0.5833333333

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 = -0.5833333333 + 1.5625

Reorder the terms:
1.5625 + 2.5c + c2 = -0.5833333333 + 1.5625

Combine like terms: -0.5833333333 + 1.5625 = 0.9791666667
1.5625 + 2.5c + c2 = 0.9791666667

Factor a perfect square on the left side:
(c + 1.25)(c + 1.25) = 0.9791666667

Calculate the square root of the right side: 0.989528507

Break this problem into two subproblems by setting 
(c + 1.25) equal to 0.989528507 and -0.989528507.

Subproblem 1

c + 1.25 = 0.989528507 Simplifying c + 1.25 = 0.989528507 Reorder the terms: 1.25 + c = 0.989528507 Solving 1.25 + c = 0.989528507 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 = 0.989528507 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + c = 0.989528507 + -1.25 c = 0.989528507 + -1.25 Combine like terms: 0.989528507 + -1.25 = -0.260471493 c = -0.260471493 Simplifying c = -0.260471493

Subproblem 2

c + 1.25 = -0.989528507 Simplifying c + 1.25 = -0.989528507 Reorder the terms: 1.25 + c = -0.989528507 Solving 1.25 + c = -0.989528507 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 = -0.989528507 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + c = -0.989528507 + -1.25 c = -0.989528507 + -1.25 Combine like terms: -0.989528507 + -1.25 = -2.239528507 c = -2.239528507 Simplifying c = -2.239528507

Solution

The solution to the problem is based on the solutions from the subproblems. c = {-0.260471493, -2.239528507}

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