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Simplifying 40 = -85.6x2 + 160x + -9.35 Reorder the terms: 40 = -9.35 + 160x + -85.6x2 Solving 40 = -9.35 + 160x + -85.6x2 Solving for variable 'x'. Combine like terms: 40 + 9.35 = 49.35 49.35 + -160x + 85.6x2 = -9.35 + 160x + -85.6x2 + 9.35 + -160x + 85.6x2 Reorder the terms: 49.35 + -160x + 85.6x2 = -9.35 + 9.35 + 160x + -160x + -85.6x2 + 85.6x2 Combine like terms: -9.35 + 9.35 = 0.00 49.35 + -160x + 85.6x2 = 0.00 + 160x + -160x + -85.6x2 + 85.6x2 49.35 + -160x + 85.6x2 = 160x + -160x + -85.6x2 + 85.6x2 Combine like terms: 160x + -160x = 0 49.35 + -160x + 85.6x2 = 0 + -85.6x2 + 85.6x2 49.35 + -160x + 85.6x2 = -85.6x2 + 85.6x2 Combine like terms: -85.6x2 + 85.6x2 = 0.0 49.35 + -160x + 85.6x2 = 0.0 Begin completing the square. Divide all terms by 85.6 the coefficient of the squared term: Divide each side by '85.6'. 0.5765186916 + -1.869158879x + x2 = 0 Move the constant term to the right: Add '-0.5765186916' to each side of the equation. 0.5765186916 + -1.869158879x + -0.5765186916 + x2 = 0 + -0.5765186916 Reorder the terms: 0.5765186916 + -0.5765186916 + -1.869158879x + x2 = 0 + -0.5765186916 Combine like terms: 0.5765186916 + -0.5765186916 = 0.0000000000 0.0000000000 + -1.869158879x + x2 = 0 + -0.5765186916 -1.869158879x + x2 = 0 + -0.5765186916 Combine like terms: 0 + -0.5765186916 = -0.5765186916 -1.869158879x + x2 = -0.5765186916 The x term is -1.869158879x. Take half its coefficient (-0.9345794395). Square it (0.8734387287) and add it to both sides. Add '0.8734387287' to each side of the equation. -1.869158879x + 0.8734387287 + x2 = -0.5765186916 + 0.8734387287 Reorder the terms: 0.8734387287 + -1.869158879x + x2 = -0.5765186916 + 0.8734387287 Combine like terms: -0.5765186916 + 0.8734387287 = 0.2969200371 0.8734387287 + -1.869158879x + x2 = 0.2969200371 Factor a perfect square on the left side: (x + -0.9345794395)(x + -0.9345794395) = 0.2969200371 Calculate the square root of the right side: 0.544903695 Break this problem into two subproblems by setting (x + -0.9345794395) equal to 0.544903695 and -0.544903695.Subproblem 1
x + -0.9345794395 = 0.544903695 Simplifying x + -0.9345794395 = 0.544903695 Reorder the terms: -0.9345794395 + x = 0.544903695 Solving -0.9345794395 + x = 0.544903695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9345794395' to each side of the equation. -0.9345794395 + 0.9345794395 + x = 0.544903695 + 0.9345794395 Combine like terms: -0.9345794395 + 0.9345794395 = 0.0000000000 0.0000000000 + x = 0.544903695 + 0.9345794395 x = 0.544903695 + 0.9345794395 Combine like terms: 0.544903695 + 0.9345794395 = 1.4794831345 x = 1.4794831345 Simplifying x = 1.4794831345Subproblem 2
x + -0.9345794395 = -0.544903695 Simplifying x + -0.9345794395 = -0.544903695 Reorder the terms: -0.9345794395 + x = -0.544903695 Solving -0.9345794395 + x = -0.544903695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9345794395' to each side of the equation. -0.9345794395 + 0.9345794395 + x = -0.544903695 + 0.9345794395 Combine like terms: -0.9345794395 + 0.9345794395 = 0.0000000000 0.0000000000 + x = -0.544903695 + 0.9345794395 x = -0.544903695 + 0.9345794395 Combine like terms: -0.544903695 + 0.9345794395 = 0.3896757445 x = 0.3896757445 Simplifying x = 0.3896757445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4794831345, 0.3896757445}
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