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Simplifying 18c4 + 57c3 + 10c2 = 0 Reorder the terms: 10c2 + 57c3 + 18c4 = 0 Solving 10c2 + 57c3 + 18c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c2'. c2(10 + 57c + 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 + 57c + 18c2)' equal to zero and attempt to solve: Simplifying 10 + 57c + 18c2 = 0 Solving 10 + 57c + 18c2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.5555555556 + 3.166666667c + c2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + 3.166666667c + -0.5555555556 + c2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + 3.166666667c + c2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + 3.166666667c + c2 = 0 + -0.5555555556 3.166666667c + c2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 3.166666667c + c2 = -0.5555555556 The c term is 3.166666667c. Take half its coefficient (1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. 3.166666667c + 2.506944447 + c2 = -0.5555555556 + 2.506944447 Reorder the terms: 2.506944447 + 3.166666667c + c2 = -0.5555555556 + 2.506944447 Combine like terms: -0.5555555556 + 2.506944447 = 1.9513888914 2.506944447 + 3.166666667c + c2 = 1.9513888914 Factor a perfect square on the left side: (c + 1.583333334)(c + 1.583333334) = 1.9513888914 Calculate the square root of the right side: 1.396921219 Break this problem into two subproblems by setting (c + 1.583333334) equal to 1.396921219 and -1.396921219.Subproblem 1
c + 1.583333334 = 1.396921219 Simplifying c + 1.583333334 = 1.396921219 Reorder the terms: 1.583333334 + c = 1.396921219 Solving 1.583333334 + c = 1.396921219 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + c = 1.396921219 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + c = 1.396921219 + -1.583333334 c = 1.396921219 + -1.583333334 Combine like terms: 1.396921219 + -1.583333334 = -0.186412115 c = -0.186412115 Simplifying c = -0.186412115Subproblem 2
c + 1.583333334 = -1.396921219 Simplifying c + 1.583333334 = -1.396921219 Reorder the terms: 1.583333334 + c = -1.396921219 Solving 1.583333334 + c = -1.396921219 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + c = -1.396921219 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + c = -1.396921219 + -1.583333334 c = -1.396921219 + -1.583333334 Combine like terms: -1.396921219 + -1.583333334 = -2.980254553 c = -2.980254553 Simplifying c = -2.980254553Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.186412115, -2.980254553}Solution
c = {0, -0.186412115, -2.980254553}
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