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Simplifying 3c(4c2 + -5) + -1c(9c) = 0 Reorder the terms: 3c(-5 + 4c2) + -1c(9c) = 0 (-5 * 3c + 4c2 * 3c) + -1c(9c) = 0 (-15c + 12c3) + -1c(9c) = 0 Remove parenthesis around (9c) -15c + 12c3 + -1c * 9c = 0 Reorder the terms for easier multiplication: -15c + 12c3 + -1 * 9c * c = 0 Multiply -1 * 9 -15c + 12c3 + -9c * c = 0 Multiply c * c -15c + 12c3 + -9c2 = 0 Reorder the terms: -15c + -9c2 + 12c3 = 0 Solving -15c + -9c2 + 12c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3c'. 3c(-5 + -3c + 4c2) = 0 Ignore the factor 3.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 '(-5 + -3c + 4c2)' equal to zero and attempt to solve: Simplifying -5 + -3c + 4c2 = 0 Solving -5 + -3c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -0.75c + c2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.75c + 1.25 + c2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.75c + c2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.75c + c2 = 0 + 1.25 -0.75c + c2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.75c + c2 = 1.25 The c term is -0.75c. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75c + 0.140625 + c2 = 1.25 + 0.140625 Reorder the terms: 0.140625 + -0.75c + c2 = 1.25 + 0.140625 Combine like terms: 1.25 + 0.140625 = 1.390625 0.140625 + -0.75c + c2 = 1.390625 Factor a perfect square on the left side: (c + -0.375)(c + -0.375) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (c + -0.375) equal to 1.179247642 and -1.179247642.Subproblem 1
c + -0.375 = 1.179247642 Simplifying c + -0.375 = 1.179247642 Reorder the terms: -0.375 + c = 1.179247642 Solving -0.375 + c = 1.179247642 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + c = 1.179247642 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + c = 1.179247642 + 0.375 c = 1.179247642 + 0.375 Combine like terms: 1.179247642 + 0.375 = 1.554247642 c = 1.554247642 Simplifying c = 1.554247642Subproblem 2
c + -0.375 = -1.179247642 Simplifying c + -0.375 = -1.179247642 Reorder the terms: -0.375 + c = -1.179247642 Solving -0.375 + c = -1.179247642 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + c = -1.179247642 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + c = -1.179247642 + 0.375 c = -1.179247642 + 0.375 Combine like terms: -1.179247642 + 0.375 = -0.804247642 c = -0.804247642 Simplifying c = -0.804247642Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.554247642, -0.804247642}Solution
c = {0, 1.554247642, -0.804247642}
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