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Simplifying 14 + -1(6 + -3c) = 4c * c 14 + (6 * -1 + -3c * -1) = 4c * c 14 + (-6 + 3c) = 4c * c Combine like terms: 14 + -6 = 8 8 + 3c = 4c * c Multiply c * c 8 + 3c = 4c2 Solving 8 + 3c = 4c2 Solving for variable 'c'. Combine like terms: 4c2 + -4c2 = 0 8 + 3c + -4c2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2 + -0.75c + c2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.75c + 2 + c2 = 0 + 2 Reorder the terms: -2 + 2 + -0.75c + c2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.75c + c2 = 0 + 2 -0.75c + c2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.75c + c2 = 2 The c term is -0.75c. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75c + 0.140625 + c2 = 2 + 0.140625 Reorder the terms: 0.140625 + -0.75c + c2 = 2 + 0.140625 Combine like terms: 2 + 0.140625 = 2.140625 0.140625 + -0.75c + c2 = 2.140625 Factor a perfect square on the left side: (c + -0.375)(c + -0.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (c + -0.375) equal to 1.463087489 and -1.463087489.Subproblem 1
c + -0.375 = 1.463087489 Simplifying c + -0.375 = 1.463087489 Reorder the terms: -0.375 + c = 1.463087489 Solving -0.375 + c = 1.463087489 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + c = 1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + c = 1.463087489 + 0.375 c = 1.463087489 + 0.375 Combine like terms: 1.463087489 + 0.375 = 1.838087489 c = 1.838087489 Simplifying c = 1.838087489Subproblem 2
c + -0.375 = -1.463087489 Simplifying c + -0.375 = -1.463087489 Reorder the terms: -0.375 + c = -1.463087489 Solving -0.375 + c = -1.463087489 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + c = -1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + c = -1.463087489 + 0.375 c = -1.463087489 + 0.375 Combine like terms: -1.463087489 + 0.375 = -1.088087489 c = -1.088087489 Simplifying c = -1.088087489Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.838087489, -1.088087489}
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