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Simplifying 3c2 + 12c + -11 = 0 Reorder the terms: -11 + 12c + 3c2 = 0 Solving -11 + 12c + 3c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + 4c + c2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 4c + 3.666666667 + c2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 4c + c2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 4c + c2 = 0 + 3.666666667 4c + c2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 4c + c2 = 3.666666667 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 = 3.666666667 + 4 Reorder the terms: 4 + 4c + c2 = 3.666666667 + 4 Combine like terms: 3.666666667 + 4 = 7.666666667 4 + 4c + c2 = 7.666666667 Factor a perfect square on the left side: (c + 2)(c + 2) = 7.666666667 Calculate the square root of the right side: 2.768874621 Break this problem into two subproblems by setting (c + 2) equal to 2.768874621 and -2.768874621.Subproblem 1
c + 2 = 2.768874621 Simplifying c + 2 = 2.768874621 Reorder the terms: 2 + c = 2.768874621 Solving 2 + c = 2.768874621 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 = 2.768874621 + -2 Combine like terms: 2 + -2 = 0 0 + c = 2.768874621 + -2 c = 2.768874621 + -2 Combine like terms: 2.768874621 + -2 = 0.768874621 c = 0.768874621 Simplifying c = 0.768874621Subproblem 2
c + 2 = -2.768874621 Simplifying c + 2 = -2.768874621 Reorder the terms: 2 + c = -2.768874621 Solving 2 + c = -2.768874621 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 = -2.768874621 + -2 Combine like terms: 2 + -2 = 0 0 + c = -2.768874621 + -2 c = -2.768874621 + -2 Combine like terms: -2.768874621 + -2 = -4.768874621 c = -4.768874621 Simplifying c = -4.768874621Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.768874621, -4.768874621}
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