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Simplifying 5 = 0.0002x2 + -0.316x + 127.9 Reorder the terms: 5 = 127.9 + -0.316x + 0.0002x2 Solving 5 = 127.9 + -0.316x + 0.0002x2 Solving for variable 'x'. Combine like terms: 5 + -127.9 = -122.9 -122.9 + 0.316x + -0.0002x2 = 127.9 + -0.316x + 0.0002x2 + -127.9 + 0.316x + -0.0002x2 Reorder the terms: -122.9 + 0.316x + -0.0002x2 = 127.9 + -127.9 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: 127.9 + -127.9 = 0.0 -122.9 + 0.316x + -0.0002x2 = 0.0 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 -122.9 + 0.316x + -0.0002x2 = -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: -0.316x + 0.316x = 0.000 -122.9 + 0.316x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2 -122.9 + 0.316x + -0.0002x2 = 0.0002x2 + -0.0002x2 Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000 -122.9 + 0.316x + -0.0002x2 = 0.0000 Begin completing the square. Divide all terms by -0.0002 the coefficient of the squared term: Divide each side by '-0.0002'. 614500 + -1580x + x2 = 0 Move the constant term to the right: Add '-614500' to each side of the equation. 614500 + -1580x + -614500 + x2 = 0 + -614500 Reorder the terms: 614500 + -614500 + -1580x + x2 = 0 + -614500 Combine like terms: 614500 + -614500 = 0 0 + -1580x + x2 = 0 + -614500 -1580x + x2 = 0 + -614500 Combine like terms: 0 + -614500 = -614500 -1580x + x2 = -614500 The x term is -1580x. Take half its coefficient (-790). Square it (624100) and add it to both sides. Add '624100' to each side of the equation. -1580x + 624100 + x2 = -614500 + 624100 Reorder the terms: 624100 + -1580x + x2 = -614500 + 624100 Combine like terms: -614500 + 624100 = 9600 624100 + -1580x + x2 = 9600 Factor a perfect square on the left side: (x + -790)(x + -790) = 9600 Calculate the square root of the right side: 97.979589711 Break this problem into two subproblems by setting (x + -790) equal to 97.979589711 and -97.979589711.Subproblem 1
x + -790 = 97.979589711 Simplifying x + -790 = 97.979589711 Reorder the terms: -790 + x = 97.979589711 Solving -790 + x = 97.979589711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = 97.979589711 + 790 Combine like terms: -790 + 790 = 0 0 + x = 97.979589711 + 790 x = 97.979589711 + 790 Combine like terms: 97.979589711 + 790 = 887.979589711 x = 887.979589711 Simplifying x = 887.979589711Subproblem 2
x + -790 = -97.979589711 Simplifying x + -790 = -97.979589711 Reorder the terms: -790 + x = -97.979589711 Solving -790 + x = -97.979589711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = -97.979589711 + 790 Combine like terms: -790 + 790 = 0 0 + x = -97.979589711 + 790 x = -97.979589711 + 790 Combine like terms: -97.979589711 + 790 = 692.020410289 x = 692.020410289 Simplifying x = 692.020410289Solution
The solution to the problem is based on the solutions from the subproblems. x = {887.979589711, 692.020410289}
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