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Simplifying 10 = -85.6x2 + 160x + -9.35 Reorder the terms: 10 = -9.35 + 160x + -85.6x2 Solving 10 = -9.35 + 160x + -85.6x2 Solving for variable 'x'. Combine like terms: 10 + 9.35 = 19.35 19.35 + -160x + 85.6x2 = -9.35 + 160x + -85.6x2 + 9.35 + -160x + 85.6x2 Reorder the terms: 19.35 + -160x + 85.6x2 = -9.35 + 9.35 + 160x + -160x + -85.6x2 + 85.6x2 Combine like terms: -9.35 + 9.35 = 0.00 19.35 + -160x + 85.6x2 = 0.00 + 160x + -160x + -85.6x2 + 85.6x2 19.35 + -160x + 85.6x2 = 160x + -160x + -85.6x2 + 85.6x2 Combine like terms: 160x + -160x = 0 19.35 + -160x + 85.6x2 = 0 + -85.6x2 + 85.6x2 19.35 + -160x + 85.6x2 = -85.6x2 + 85.6x2 Combine like terms: -85.6x2 + 85.6x2 = 0.0 19.35 + -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'. 0.2260514019 + -1.869158879x + x2 = 0 Move the constant term to the right: Add '-0.2260514019' to each side of the equation. 0.2260514019 + -1.869158879x + -0.2260514019 + x2 = 0 + -0.2260514019 Reorder the terms: 0.2260514019 + -0.2260514019 + -1.869158879x + x2 = 0 + -0.2260514019 Combine like terms: 0.2260514019 + -0.2260514019 = 0.0000000000 0.0000000000 + -1.869158879x + x2 = 0 + -0.2260514019 -1.869158879x + x2 = 0 + -0.2260514019 Combine like terms: 0 + -0.2260514019 = -0.2260514019 -1.869158879x + x2 = -0.2260514019 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 = -0.2260514019 + 0.8734387287 Reorder the terms: 0.8734387287 + -1.869158879x + x2 = -0.2260514019 + 0.8734387287 Combine like terms: -0.2260514019 + 0.8734387287 = 0.6473873268 0.8734387287 + -1.869158879x + x2 = 0.6473873268 Factor a perfect square on the left side: (x + -0.9345794395)(x + -0.9345794395) = 0.6473873268 Calculate the square root of the right side: 0.804603832 Break this problem into two subproblems by setting (x + -0.9345794395) equal to 0.804603832 and -0.804603832.Subproblem 1
x + -0.9345794395 = 0.804603832 Simplifying x + -0.9345794395 = 0.804603832 Reorder the terms: -0.9345794395 + x = 0.804603832 Solving -0.9345794395 + x = 0.804603832 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 = 0.804603832 + 0.9345794395 Combine like terms: -0.9345794395 + 0.9345794395 = 0.0000000000 0.0000000000 + x = 0.804603832 + 0.9345794395 x = 0.804603832 + 0.9345794395 Combine like terms: 0.804603832 + 0.9345794395 = 1.7391832715 x = 1.7391832715 Simplifying x = 1.7391832715Subproblem 2
x + -0.9345794395 = -0.804603832 Simplifying x + -0.9345794395 = -0.804603832 Reorder the terms: -0.9345794395 + x = -0.804603832 Solving -0.9345794395 + x = -0.804603832 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 = -0.804603832 + 0.9345794395 Combine like terms: -0.9345794395 + 0.9345794395 = 0.0000000000 0.0000000000 + x = -0.804603832 + 0.9345794395 x = -0.804603832 + 0.9345794395 Combine like terms: -0.804603832 + 0.9345794395 = 0.1299756075 x = 0.1299756075 Simplifying x = 0.1299756075Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7391832715, 0.1299756075}
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