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Simplifying c3 + 2c2 + -5c = 0 Reorder the terms: -5c + 2c2 + c3 = 0 Solving -5c + 2c2 + c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c'. c(-5 + 2c + c2) = 0Subproblem 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 '(-5 + 2c + c2)' equal to zero and attempt to solve: Simplifying -5 + 2c + c2 = 0 Solving -5 + 2c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2c + 5 + c2 = 0 + 5 Reorder the terms: -5 + 5 + 2c + c2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2c + c2 = 0 + 5 2c + c2 = 0 + 5 Combine like terms: 0 + 5 = 5 2c + c2 = 5 The c term is 2c. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2c + 1 + c2 = 5 + 1 Reorder the terms: 1 + 2c + c2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2c + c2 = 6 Factor a perfect square on the left side: (c + 1)(c + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (c + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
c + 1 = 2.449489743 Simplifying c + 1 = 2.449489743 Reorder the terms: 1 + c = 2.449489743 Solving 1 + c = 2.449489743 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + c = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + c = 2.449489743 + -1 c = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 c = 1.449489743 Simplifying c = 1.449489743Subproblem 2
c + 1 = -2.449489743 Simplifying c + 1 = -2.449489743 Reorder the terms: 1 + c = -2.449489743 Solving 1 + c = -2.449489743 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + c = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + c = -2.449489743 + -1 c = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 c = -3.449489743 Simplifying c = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.449489743, -3.449489743}Solution
c = {0, 1.449489743, -3.449489743}
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