22579=4c^2+1840c

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Solution for 22579=4c^2+1840c equation:


Simplifying
22579 = 4c2 + 1840c

Reorder the terms:
22579 = 1840c + 4c2

Solving
22579 = 1840c + 4c2

Solving for variable 'c'.

Reorder the terms:
22579 + -1840c + -4c2 = 1840c + -1840c + 4c2 + -4c2

Combine like terms: 1840c + -1840c = 0
22579 + -1840c + -4c2 = 0 + 4c2 + -4c2
22579 + -1840c + -4c2 = 4c2 + -4c2

Combine like terms: 4c2 + -4c2 = 0
22579 + -1840c + -4c2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-5644.75 + 460c + c2 = 0

Move the constant term to the right:

Add '5644.75' to each side of the equation.
-5644.75 + 460c + 5644.75 + c2 = 0 + 5644.75

Reorder the terms:
-5644.75 + 5644.75 + 460c + c2 = 0 + 5644.75

Combine like terms: -5644.75 + 5644.75 = 0.00
0.00 + 460c + c2 = 0 + 5644.75
460c + c2 = 0 + 5644.75

Combine like terms: 0 + 5644.75 = 5644.75
460c + c2 = 5644.75

The c term is 460c.  Take half its coefficient (230).
Square it (52900) and add it to both sides.

Add '52900' to each side of the equation.
460c + 52900 + c2 = 5644.75 + 52900

Reorder the terms:
52900 + 460c + c2 = 5644.75 + 52900

Combine like terms: 5644.75 + 52900 = 58544.75
52900 + 460c + c2 = 58544.75

Factor a perfect square on the left side:
(c + 230)(c + 230) = 58544.75

Calculate the square root of the right side: 241.960224004

Break this problem into two subproblems by setting 
(c + 230) equal to 241.960224004 and -241.960224004.

Subproblem 1

c + 230 = 241.960224004 Simplifying c + 230 = 241.960224004 Reorder the terms: 230 + c = 241.960224004 Solving 230 + c = 241.960224004 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-230' to each side of the equation. 230 + -230 + c = 241.960224004 + -230 Combine like terms: 230 + -230 = 0 0 + c = 241.960224004 + -230 c = 241.960224004 + -230 Combine like terms: 241.960224004 + -230 = 11.960224004 c = 11.960224004 Simplifying c = 11.960224004

Subproblem 2

c + 230 = -241.960224004 Simplifying c + 230 = -241.960224004 Reorder the terms: 230 + c = -241.960224004 Solving 230 + c = -241.960224004 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-230' to each side of the equation. 230 + -230 + c = -241.960224004 + -230 Combine like terms: 230 + -230 = 0 0 + c = -241.960224004 + -230 c = -241.960224004 + -230 Combine like terms: -241.960224004 + -230 = -471.960224004 c = -471.960224004 Simplifying c = -471.960224004

Solution

The solution to the problem is based on the solutions from the subproblems. c = {11.960224004, -471.960224004}

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