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Simplifying 20 = -1.1x2 + 10.9x + -5.6 Reorder the terms: 20 = -5.6 + 10.9x + -1.1x2 Solving 20 = -5.6 + 10.9x + -1.1x2 Solving for variable 'x'. Combine like terms: 20 + 5.6 = 25.6 25.6 + -10.9x + 1.1x2 = -5.6 + 10.9x + -1.1x2 + 5.6 + -10.9x + 1.1x2 Reorder the terms: 25.6 + -10.9x + 1.1x2 = -5.6 + 5.6 + 10.9x + -10.9x + -1.1x2 + 1.1x2 Combine like terms: -5.6 + 5.6 = 0.0 25.6 + -10.9x + 1.1x2 = 0.0 + 10.9x + -10.9x + -1.1x2 + 1.1x2 25.6 + -10.9x + 1.1x2 = 10.9x + -10.9x + -1.1x2 + 1.1x2 Combine like terms: 10.9x + -10.9x = 0.0 25.6 + -10.9x + 1.1x2 = 0.0 + -1.1x2 + 1.1x2 25.6 + -10.9x + 1.1x2 = -1.1x2 + 1.1x2 Combine like terms: -1.1x2 + 1.1x2 = 0.0 25.6 + -10.9x + 1.1x2 = 0.0 Begin completing the square. Divide all terms by 1.1 the coefficient of the squared term: Divide each side by '1.1'. 23.27272727 + -9.909090909x + x2 = 0 Move the constant term to the right: Add '-23.27272727' to each side of the equation. 23.27272727 + -9.909090909x + -23.27272727 + x2 = 0 + -23.27272727 Reorder the terms: 23.27272727 + -23.27272727 + -9.909090909x + x2 = 0 + -23.27272727 Combine like terms: 23.27272727 + -23.27272727 = 0.00000000 0.00000000 + -9.909090909x + x2 = 0 + -23.27272727 -9.909090909x + x2 = 0 + -23.27272727 Combine like terms: 0 + -23.27272727 = -23.27272727 -9.909090909x + x2 = -23.27272727 The x term is -9.909090909x. Take half its coefficient (-4.954545455). Square it (24.54752067) and add it to both sides. Add '24.54752067' to each side of the equation. -9.909090909x + 24.54752067 + x2 = -23.27272727 + 24.54752067 Reorder the terms: 24.54752067 + -9.909090909x + x2 = -23.27272727 + 24.54752067 Combine like terms: -23.27272727 + 24.54752067 = 1.2747934 24.54752067 + -9.909090909x + x2 = 1.2747934 Factor a perfect square on the left side: (x + -4.954545455)(x + -4.954545455) = 1.2747934 Calculate the square root of the right side: 1.129067491 Break this problem into two subproblems by setting (x + -4.954545455) equal to 1.129067491 and -1.129067491.Subproblem 1
x + -4.954545455 = 1.129067491 Simplifying x + -4.954545455 = 1.129067491 Reorder the terms: -4.954545455 + x = 1.129067491 Solving -4.954545455 + x = 1.129067491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.954545455' to each side of the equation. -4.954545455 + 4.954545455 + x = 1.129067491 + 4.954545455 Combine like terms: -4.954545455 + 4.954545455 = 0.000000000 0.000000000 + x = 1.129067491 + 4.954545455 x = 1.129067491 + 4.954545455 Combine like terms: 1.129067491 + 4.954545455 = 6.083612946 x = 6.083612946 Simplifying x = 6.083612946Subproblem 2
x + -4.954545455 = -1.129067491 Simplifying x + -4.954545455 = -1.129067491 Reorder the terms: -4.954545455 + x = -1.129067491 Solving -4.954545455 + x = -1.129067491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.954545455' to each side of the equation. -4.954545455 + 4.954545455 + x = -1.129067491 + 4.954545455 Combine like terms: -4.954545455 + 4.954545455 = 0.000000000 0.000000000 + x = -1.129067491 + 4.954545455 x = -1.129067491 + 4.954545455 Combine like terms: -1.129067491 + 4.954545455 = 3.825477964 x = 3.825477964 Simplifying x = 3.825477964Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.083612946, 3.825477964}
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