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Simplifying (6c2 + 2c + -8) + -1(8c2 + c + -13) = 0 Reorder the terms: (-8 + 2c + 6c2) + -1(8c2 + c + -13) = 0 Remove parenthesis around (-8 + 2c + 6c2) -8 + 2c + 6c2 + -1(8c2 + c + -13) = 0 Reorder the terms: -8 + 2c + 6c2 + -1(-13 + c + 8c2) = 0 -8 + 2c + 6c2 + (-13 * -1 + c * -1 + 8c2 * -1) = 0 -8 + 2c + 6c2 + (13 + -1c + -8c2) = 0 Reorder the terms: -8 + 13 + 2c + -1c + 6c2 + -8c2 = 0 Combine like terms: -8 + 13 = 5 5 + 2c + -1c + 6c2 + -8c2 = 0 Combine like terms: 2c + -1c = 1c 5 + 1c + 6c2 + -8c2 = 0 Combine like terms: 6c2 + -8c2 = -2c2 5 + 1c + -2c2 = 0 Solving 5 + 1c + -2c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -0.5c + c2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.5c + 2.5 + c2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.5c + c2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.5c + c2 = 0 + 2.5 -0.5c + c2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.5c + c2 = 2.5 The c term is -0.5c. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5c + 0.0625 + c2 = 2.5 + 0.0625 Reorder the terms: 0.0625 + -0.5c + c2 = 2.5 + 0.0625 Combine like terms: 2.5 + 0.0625 = 2.5625 0.0625 + -0.5c + c2 = 2.5625 Factor a perfect square on the left side: (c + -0.25)(c + -0.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (c + -0.25) equal to 1.600781059 and -1.600781059.Subproblem 1
c + -0.25 = 1.600781059 Simplifying c + -0.25 = 1.600781059 Reorder the terms: -0.25 + c = 1.600781059 Solving -0.25 + c = 1.600781059 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + c = 1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + c = 1.600781059 + 0.25 c = 1.600781059 + 0.25 Combine like terms: 1.600781059 + 0.25 = 1.850781059 c = 1.850781059 Simplifying c = 1.850781059Subproblem 2
c + -0.25 = -1.600781059 Simplifying c + -0.25 = -1.600781059 Reorder the terms: -0.25 + c = -1.600781059 Solving -0.25 + c = -1.600781059 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + c = -1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + c = -1.600781059 + 0.25 c = -1.600781059 + 0.25 Combine like terms: -1.600781059 + 0.25 = -1.350781059 c = -1.350781059 Simplifying c = -1.350781059Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.850781059, -1.350781059}
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