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Simplifying 8c(4 + -1c) = 12 (4 * 8c + -1c * 8c) = 12 (32c + -8c2) = 12 Solving 32c + -8c2 = 12 Solving for variable 'c'. Reorder the terms: -12 + 32c + -8c2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 32c + -8c2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + 8c + -2c2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + 8c + -2c2)' equal to zero and attempt to solve: Simplifying -3 + 8c + -2c2 = 0 Solving -3 + 8c + -2c2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -4c + c2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4c + -1.5 + c2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4c + c2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4c + c2 = 0 + -1.5 -4c + c2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4c + c2 = -1.5 The c term is -4c. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c + 4 + c2 = -1.5 + 4 Reorder the terms: 4 + -4c + c2 = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 4 + -4c + c2 = 2.5 Factor a perfect square on the left side: (c + -2)(c + -2) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (c + -2) equal to 1.58113883 and -1.58113883.Subproblem 1
c + -2 = 1.58113883 Simplifying c + -2 = 1.58113883 Reorder the terms: -2 + c = 1.58113883 Solving -2 + c = 1.58113883 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = 1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + c = 1.58113883 + 2 c = 1.58113883 + 2 Combine like terms: 1.58113883 + 2 = 3.58113883 c = 3.58113883 Simplifying c = 3.58113883Subproblem 2
c + -2 = -1.58113883 Simplifying c + -2 = -1.58113883 Reorder the terms: -2 + c = -1.58113883 Solving -2 + c = -1.58113883 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = -1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + c = -1.58113883 + 2 c = -1.58113883 + 2 Combine like terms: -1.58113883 + 2 = 0.41886117 c = 0.41886117 Simplifying c = 0.41886117Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.58113883, 0.41886117}Solution
c = {3.58113883, 0.41886117}
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