-20c^2+50c=8c^3

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Solution for -20c^2+50c=8c^3 equation:


Simplifying
-20c2 + 50c = 8c3

Reorder the terms:
50c + -20c2 = 8c3

Solving
50c + -20c2 = 8c3

Solving for variable 'c'.

Combine like terms: 8c3 + -8c3 = 0
50c + -20c2 + -8c3 = 0

Factor out the Greatest Common Factor (GCF), '2c'.
2c(25 + -10c + -4c2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0

Subproblem 2

Set the factor '(25 + -10c + -4c2)' equal to zero and attempt to solve: Simplifying 25 + -10c + -4c2 = 0 Solving 25 + -10c + -4c2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + 2.5c + c2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 2.5c + 6.25 + c2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 2.5c + c2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 2.5c + c2 = 0 + 6.25 2.5c + c2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 2.5c + c2 = 6.25 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 = 6.25 + 1.5625 Reorder the terms: 1.5625 + 2.5c + c2 = 6.25 + 1.5625 Combine like terms: 6.25 + 1.5625 = 7.8125 1.5625 + 2.5c + c2 = 7.8125 Factor a perfect square on the left side: (c + 1.25)(c + 1.25) = 7.8125 Calculate the square root of the right side: 2.795084972 Break this problem into two subproblems by setting (c + 1.25) equal to 2.795084972 and -2.795084972.

Subproblem 1

c + 1.25 = 2.795084972 Simplifying c + 1.25 = 2.795084972 Reorder the terms: 1.25 + c = 2.795084972 Solving 1.25 + c = 2.795084972 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 = 2.795084972 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + c = 2.795084972 + -1.25 c = 2.795084972 + -1.25 Combine like terms: 2.795084972 + -1.25 = 1.545084972 c = 1.545084972 Simplifying c = 1.545084972

Subproblem 2

c + 1.25 = -2.795084972 Simplifying c + 1.25 = -2.795084972 Reorder the terms: 1.25 + c = -2.795084972 Solving 1.25 + c = -2.795084972 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 = -2.795084972 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + c = -2.795084972 + -1.25 c = -2.795084972 + -1.25 Combine like terms: -2.795084972 + -1.25 = -4.045084972 c = -4.045084972 Simplifying c = -4.045084972

Solution

The solution to the problem is based on the solutions from the subproblems. c = {1.545084972, -4.045084972}

Solution

c = {0, 1.545084972, -4.045084972}

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