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Simplifying 10c3 + -22c2 + 4c = 2c Reorder the terms: 4c + -22c2 + 10c3 = 2c Solving 4c + -22c2 + 10c3 = 2c Solving for variable 'c'. Reorder the terms: 4c + -2c + -22c2 + 10c3 = 2c + -2c Combine like terms: 4c + -2c = 2c 2c + -22c2 + 10c3 = 2c + -2c Combine like terms: 2c + -2c = 0 2c + -22c2 + 10c3 = 0 Factor out the Greatest Common Factor (GCF), '2c'. 2c(1 + -11c + 5c2) = 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 = 0Subproblem 2
Set the factor '(1 + -11c + 5c2)' equal to zero and attempt to solve: Simplifying 1 + -11c + 5c2 = 0 Solving 1 + -11c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -2.2c + c2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -2.2c + -0.2 + c2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -2.2c + c2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -2.2c + c2 = 0 + -0.2 -2.2c + c2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -2.2c + c2 = -0.2 The c term is -2.2c. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2c + 1.21 + c2 = -0.2 + 1.21 Reorder the terms: 1.21 + -2.2c + c2 = -0.2 + 1.21 Combine like terms: -0.2 + 1.21 = 1.01 1.21 + -2.2c + c2 = 1.01 Factor a perfect square on the left side: (c + -1.1)(c + -1.1) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (c + -1.1) equal to 1.004987562 and -1.004987562.Subproblem 1
c + -1.1 = 1.004987562 Simplifying c + -1.1 = 1.004987562 Reorder the terms: -1.1 + c = 1.004987562 Solving -1.1 + c = 1.004987562 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + c = 1.004987562 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + c = 1.004987562 + 1.1 c = 1.004987562 + 1.1 Combine like terms: 1.004987562 + 1.1 = 2.104987562 c = 2.104987562 Simplifying c = 2.104987562Subproblem 2
c + -1.1 = -1.004987562 Simplifying c + -1.1 = -1.004987562 Reorder the terms: -1.1 + c = -1.004987562 Solving -1.1 + c = -1.004987562 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + c = -1.004987562 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + c = -1.004987562 + 1.1 c = -1.004987562 + 1.1 Combine like terms: -1.004987562 + 1.1 = 0.095012438 c = 0.095012438 Simplifying c = 0.095012438Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.104987562, 0.095012438}Solution
c = {0, 2.104987562, 0.095012438}
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