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Simplifying 18c4 + 23c3 + -10c2 = 0 Reorder the terms: -10c2 + 23c3 + 18c4 = 0 Solving -10c2 + 23c3 + 18c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c2'. c2(-10 + 23c + 18c2) = 0Subproblem 1
Set the factor 'c2' equal to zero and attempt to solve: Simplifying c2 = 0 Solving c2 = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c2 = 0 Take the square root of each side: c = {0}Subproblem 2
Set the factor '(-10 + 23c + 18c2)' equal to zero and attempt to solve: Simplifying -10 + 23c + 18c2 = 0 Solving -10 + 23c + 18c2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.5555555556 + 1.277777778c + c2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 1.277777778c + 0.5555555556 + c2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 1.277777778c + c2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 1.277777778c + c2 = 0 + 0.5555555556 1.277777778c + c2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 1.277777778c + c2 = 0.5555555556 The c term is 1.277777778c. Take half its coefficient (0.638888889). Square it (0.4081790125) and add it to both sides. Add '0.4081790125' to each side of the equation. 1.277777778c + 0.4081790125 + c2 = 0.5555555556 + 0.4081790125 Reorder the terms: 0.4081790125 + 1.277777778c + c2 = 0.5555555556 + 0.4081790125 Combine like terms: 0.5555555556 + 0.4081790125 = 0.9637345681 0.4081790125 + 1.277777778c + c2 = 0.9637345681 Factor a perfect square on the left side: (c + 0.638888889)(c + 0.638888889) = 0.9637345681 Calculate the square root of the right side: 0.981699836 Break this problem into two subproblems by setting (c + 0.638888889) equal to 0.981699836 and -0.981699836.Subproblem 1
c + 0.638888889 = 0.981699836 Simplifying c + 0.638888889 = 0.981699836 Reorder the terms: 0.638888889 + c = 0.981699836 Solving 0.638888889 + c = 0.981699836 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.638888889' to each side of the equation. 0.638888889 + -0.638888889 + c = 0.981699836 + -0.638888889 Combine like terms: 0.638888889 + -0.638888889 = 0.000000000 0.000000000 + c = 0.981699836 + -0.638888889 c = 0.981699836 + -0.638888889 Combine like terms: 0.981699836 + -0.638888889 = 0.342810947 c = 0.342810947 Simplifying c = 0.342810947Subproblem 2
c + 0.638888889 = -0.981699836 Simplifying c + 0.638888889 = -0.981699836 Reorder the terms: 0.638888889 + c = -0.981699836 Solving 0.638888889 + c = -0.981699836 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.638888889' to each side of the equation. 0.638888889 + -0.638888889 + c = -0.981699836 + -0.638888889 Combine like terms: 0.638888889 + -0.638888889 = 0.000000000 0.000000000 + c = -0.981699836 + -0.638888889 c = -0.981699836 + -0.638888889 Combine like terms: -0.981699836 + -0.638888889 = -1.620588725 c = -1.620588725 Simplifying c = -1.620588725Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.342810947, -1.620588725}Solution
c = {0, 0.342810947, -1.620588725}
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