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Simplifying 2c2 + -12c + 6 = 0 Reorder the terms: 6 + -12c + 2c2 = 0 Solving 6 + -12c + 2c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -6c + c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -6c + c2)' equal to zero and attempt to solve: Simplifying 3 + -6c + c2 = 0 Solving 3 + -6c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6c + -3 + c2 = 0 + -3 Reorder the terms: 3 + -3 + -6c + c2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6c + c2 = 0 + -3 -6c + c2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6c + c2 = -3 The c term is -6c. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6c + 9 + c2 = -3 + 9 Reorder the terms: 9 + -6c + c2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6c + c2 = 6 Factor a perfect square on the left side: (c + -3)(c + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (c + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
c + -3 = 2.449489743 Simplifying c + -3 = 2.449489743 Reorder the terms: -3 + c = 2.449489743 Solving -3 + c = 2.449489743 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + c = 2.449489743 + 3 c = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 c = 5.449489743 Simplifying c = 5.449489743Subproblem 2
c + -3 = -2.449489743 Simplifying c + -3 = -2.449489743 Reorder the terms: -3 + c = -2.449489743 Solving -3 + c = -2.449489743 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + c = -2.449489743 + 3 c = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 c = 0.550510257 Simplifying c = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.449489743, 0.550510257}Solution
c = {5.449489743, 0.550510257}
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