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Simplifying c(c2 + -12c + 5) = 0 Reorder the terms: c(5 + -12c + c2) = 0 (5 * c + -12c * c + c2 * c) = 0 (5c + -12c2 + c3) = 0 Solving 5c + -12c2 + c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c'. c(5 + -12c + 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 + -12c + c2)' equal to zero and attempt to solve: Simplifying 5 + -12c + c2 = 0 Solving 5 + -12c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -12c + -5 + c2 = 0 + -5 Reorder the terms: 5 + -5 + -12c + c2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -12c + c2 = 0 + -5 -12c + c2 = 0 + -5 Combine like terms: 0 + -5 = -5 -12c + c2 = -5 The c term is -12c. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12c + 36 + c2 = -5 + 36 Reorder the terms: 36 + -12c + c2 = -5 + 36 Combine like terms: -5 + 36 = 31 36 + -12c + c2 = 31 Factor a perfect square on the left side: (c + -6)(c + -6) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (c + -6) equal to 5.567764363 and -5.567764363.Subproblem 1
c + -6 = 5.567764363 Simplifying c + -6 = 5.567764363 Reorder the terms: -6 + c = 5.567764363 Solving -6 + c = 5.567764363 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + c = 5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + c = 5.567764363 + 6 c = 5.567764363 + 6 Combine like terms: 5.567764363 + 6 = 11.567764363 c = 11.567764363 Simplifying c = 11.567764363Subproblem 2
c + -6 = -5.567764363 Simplifying c + -6 = -5.567764363 Reorder the terms: -6 + c = -5.567764363 Solving -6 + c = -5.567764363 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + c = -5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + c = -5.567764363 + 6 c = -5.567764363 + 6 Combine like terms: -5.567764363 + 6 = 0.432235637 c = 0.432235637 Simplifying c = 0.432235637Solution
The solution to the problem is based on the solutions from the subproblems. c = {11.567764363, 0.432235637}Solution
c = {0, 11.567764363, 0.432235637}
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