1436400=c(500c+8208)

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Solution for 1436400=c(500c+8208) equation:


Simplifying
1436400 = c(500c + 8208)

Reorder the terms:
1436400 = c(8208 + 500c)
1436400 = (8208 * c + 500c * c)
1436400 = (8208c + 500c2)

Solving
1436400 = 8208c + 500c2

Solving for variable 'c'.

Reorder the terms:
1436400 + -8208c + -500c2 = 8208c + -8208c + 500c2 + -500c2

Combine like terms: 8208c + -8208c = 0
1436400 + -8208c + -500c2 = 0 + 500c2 + -500c2
1436400 + -8208c + -500c2 = 500c2 + -500c2

Combine like terms: 500c2 + -500c2 = 0
1436400 + -8208c + -500c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(359100 + -2052c + -125c2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(359100 + -2052c + -125c2)' equal to zero and attempt to solve: Simplifying 359100 + -2052c + -125c2 = 0 Solving 359100 + -2052c + -125c2 = 0 Begin completing the square. Divide all terms by -125 the coefficient of the squared term: Divide each side by '-125'. -2872.8 + 16.416c + c2 = 0 Move the constant term to the right: Add '2872.8' to each side of the equation. -2872.8 + 16.416c + 2872.8 + c2 = 0 + 2872.8 Reorder the terms: -2872.8 + 2872.8 + 16.416c + c2 = 0 + 2872.8 Combine like terms: -2872.8 + 2872.8 = 0.0 0.0 + 16.416c + c2 = 0 + 2872.8 16.416c + c2 = 0 + 2872.8 Combine like terms: 0 + 2872.8 = 2872.8 16.416c + c2 = 2872.8 The c term is 16.416c. Take half its coefficient (8.208). Square it (67.371264) and add it to both sides. Add '67.371264' to each side of the equation. 16.416c + 67.371264 + c2 = 2872.8 + 67.371264 Reorder the terms: 67.371264 + 16.416c + c2 = 2872.8 + 67.371264 Combine like terms: 2872.8 + 67.371264 = 2940.171264 67.371264 + 16.416c + c2 = 2940.171264 Factor a perfect square on the left side: (c + 8.208)(c + 8.208) = 2940.171264 Calculate the square root of the right side: 54.223346116 Break this problem into two subproblems by setting (c + 8.208) equal to 54.223346116 and -54.223346116.

Subproblem 1

c + 8.208 = 54.223346116 Simplifying c + 8.208 = 54.223346116 Reorder the terms: 8.208 + c = 54.223346116 Solving 8.208 + c = 54.223346116 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-8.208' to each side of the equation. 8.208 + -8.208 + c = 54.223346116 + -8.208 Combine like terms: 8.208 + -8.208 = 0.000 0.000 + c = 54.223346116 + -8.208 c = 54.223346116 + -8.208 Combine like terms: 54.223346116 + -8.208 = 46.015346116 c = 46.015346116 Simplifying c = 46.015346116

Subproblem 2

c + 8.208 = -54.223346116 Simplifying c + 8.208 = -54.223346116 Reorder the terms: 8.208 + c = -54.223346116 Solving 8.208 + c = -54.223346116 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-8.208' to each side of the equation. 8.208 + -8.208 + c = -54.223346116 + -8.208 Combine like terms: 8.208 + -8.208 = 0.000 0.000 + c = -54.223346116 + -8.208 c = -54.223346116 + -8.208 Combine like terms: -54.223346116 + -8.208 = -62.431346116 c = -62.431346116 Simplifying c = -62.431346116

Solution

The solution to the problem is based on the solutions from the subproblems. c = {46.015346116, -62.431346116}

Solution

c = {46.015346116, -62.431346116}

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