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Simplifying 11c2 + 12c + -10 = 0 Reorder the terms: -10 + 12c + 11c2 = 0 Solving -10 + 12c + 11c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.9090909091 + 1.090909091c + c2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + 1.090909091c + 0.9090909091 + c2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + 1.090909091c + c2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + 1.090909091c + c2 = 0 + 0.9090909091 1.090909091c + c2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 1.090909091c + c2 = 0.9090909091 The c term is 1.090909091c. Take half its coefficient (0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. 1.090909091c + 0.2975206612 + c2 = 0.9090909091 + 0.2975206612 Reorder the terms: 0.2975206612 + 1.090909091c + c2 = 0.9090909091 + 0.2975206612 Combine like terms: 0.9090909091 + 0.2975206612 = 1.2066115703 0.2975206612 + 1.090909091c + c2 = 1.2066115703 Factor a perfect square on the left side: (c + 0.5454545455)(c + 0.5454545455) = 1.2066115703 Calculate the square root of the right side: 1.098458725 Break this problem into two subproblems by setting (c + 0.5454545455) equal to 1.098458725 and -1.098458725.Subproblem 1
c + 0.5454545455 = 1.098458725 Simplifying c + 0.5454545455 = 1.098458725 Reorder the terms: 0.5454545455 + c = 1.098458725 Solving 0.5454545455 + c = 1.098458725 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + c = 1.098458725 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + c = 1.098458725 + -0.5454545455 c = 1.098458725 + -0.5454545455 Combine like terms: 1.098458725 + -0.5454545455 = 0.5530041795 c = 0.5530041795 Simplifying c = 0.5530041795Subproblem 2
c + 0.5454545455 = -1.098458725 Simplifying c + 0.5454545455 = -1.098458725 Reorder the terms: 0.5454545455 + c = -1.098458725 Solving 0.5454545455 + c = -1.098458725 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + c = -1.098458725 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + c = -1.098458725 + -0.5454545455 c = -1.098458725 + -0.5454545455 Combine like terms: -1.098458725 + -0.5454545455 = -1.6439132705 c = -1.6439132705 Simplifying c = -1.6439132705Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.5530041795, -1.6439132705}
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