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Simplifying (3c2 + -8c + 5) + (c2 + -8c + -6) = 0 Reorder the terms: (5 + -8c + 3c2) + (c2 + -8c + -6) = 0 Remove parenthesis around (5 + -8c + 3c2) 5 + -8c + 3c2 + (c2 + -8c + -6) = 0 Reorder the terms: 5 + -8c + 3c2 + (-6 + -8c + c2) = 0 Remove parenthesis around (-6 + -8c + c2) 5 + -8c + 3c2 + -6 + -8c + c2 = 0 Reorder the terms: 5 + -6 + -8c + -8c + 3c2 + c2 = 0 Combine like terms: 5 + -6 = -1 -1 + -8c + -8c + 3c2 + c2 = 0 Combine like terms: -8c + -8c = -16c -1 + -16c + 3c2 + c2 = 0 Combine like terms: 3c2 + c2 = 4c2 -1 + -16c + 4c2 = 0 Solving -1 + -16c + 4c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -4c + c2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -4c + 0.25 + c2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -4c + c2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -4c + c2 = 0 + 0.25 -4c + c2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -4c + c2 = 0.25 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 = 0.25 + 4 Reorder the terms: 4 + -4c + c2 = 0.25 + 4 Combine like terms: 0.25 + 4 = 4.25 4 + -4c + c2 = 4.25 Factor a perfect square on the left side: (c + -2)(c + -2) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (c + -2) equal to 2.061552813 and -2.061552813.Subproblem 1
c + -2 = 2.061552813 Simplifying c + -2 = 2.061552813 Reorder the terms: -2 + c = 2.061552813 Solving -2 + c = 2.061552813 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 = 2.061552813 + 2 Combine like terms: -2 + 2 = 0 0 + c = 2.061552813 + 2 c = 2.061552813 + 2 Combine like terms: 2.061552813 + 2 = 4.061552813 c = 4.061552813 Simplifying c = 4.061552813Subproblem 2
c + -2 = -2.061552813 Simplifying c + -2 = -2.061552813 Reorder the terms: -2 + c = -2.061552813 Solving -2 + c = -2.061552813 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 = -2.061552813 + 2 Combine like terms: -2 + 2 = 0 0 + c = -2.061552813 + 2 c = -2.061552813 + 2 Combine like terms: -2.061552813 + 2 = -0.061552813 c = -0.061552813 Simplifying c = -0.061552813Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.061552813, -0.061552813}
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