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Simplifying 3c2 + 30c + -36 = 0 Reorder the terms: -36 + 30c + 3c2 = 0 Solving -36 + 30c + 3c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + 10c + c2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + 10c + c2)' equal to zero and attempt to solve: Simplifying -12 + 10c + c2 = 0 Solving -12 + 10c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 10c + 12 + c2 = 0 + 12 Reorder the terms: -12 + 12 + 10c + c2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 10c + c2 = 0 + 12 10c + c2 = 0 + 12 Combine like terms: 0 + 12 = 12 10c + c2 = 12 The c term is 10c. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10c + 25 + c2 = 12 + 25 Reorder the terms: 25 + 10c + c2 = 12 + 25 Combine like terms: 12 + 25 = 37 25 + 10c + c2 = 37 Factor a perfect square on the left side: (c + 5)(c + 5) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (c + 5) equal to 6.08276253 and -6.08276253.Subproblem 1
c + 5 = 6.08276253 Simplifying c + 5 = 6.08276253 Reorder the terms: 5 + c = 6.08276253 Solving 5 + c = 6.08276253 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + c = 6.08276253 + -5 Combine like terms: 5 + -5 = 0 0 + c = 6.08276253 + -5 c = 6.08276253 + -5 Combine like terms: 6.08276253 + -5 = 1.08276253 c = 1.08276253 Simplifying c = 1.08276253Subproblem 2
c + 5 = -6.08276253 Simplifying c + 5 = -6.08276253 Reorder the terms: 5 + c = -6.08276253 Solving 5 + c = -6.08276253 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + c = -6.08276253 + -5 Combine like terms: 5 + -5 = 0 0 + c = -6.08276253 + -5 c = -6.08276253 + -5 Combine like terms: -6.08276253 + -5 = -11.08276253 c = -11.08276253 Simplifying c = -11.08276253Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.08276253, -11.08276253}Solution
c = {1.08276253, -11.08276253}
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