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Simplifying 10000x = 80 + 4x + 0.1x2 Solving 10000x = 80 + 4x + 0.1x2 Solving for variable 'x'. Reorder the terms: -80 + 10000x + -4x + -0.1x2 = 80 + 4x + 0.1x2 + -80 + -4x + -0.1x2 Combine like terms: 10000x + -4x = 9996x -80 + 9996x + -0.1x2 = 80 + 4x + 0.1x2 + -80 + -4x + -0.1x2 Reorder the terms: -80 + 9996x + -0.1x2 = 80 + -80 + 4x + -4x + 0.1x2 + -0.1x2 Combine like terms: 80 + -80 = 0 -80 + 9996x + -0.1x2 = 0 + 4x + -4x + 0.1x2 + -0.1x2 -80 + 9996x + -0.1x2 = 4x + -4x + 0.1x2 + -0.1x2 Combine like terms: 4x + -4x = 0 -80 + 9996x + -0.1x2 = 0 + 0.1x2 + -0.1x2 -80 + 9996x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -80 + 9996x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 800 + -99960x + x2 = 0 Move the constant term to the right: Add '-800' to each side of the equation. 800 + -99960x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + -99960x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + -99960x + x2 = 0 + -800 -99960x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 -99960x + x2 = -800 The x term is -99960x. Take half its coefficient (-49980). Square it (2498000400) and add it to both sides. Add '2498000400' to each side of the equation. -99960x + 2498000400 + x2 = -800 + 2498000400 Reorder the terms: 2498000400 + -99960x + x2 = -800 + 2498000400 Combine like terms: -800 + 2498000400 = 2497999600 2498000400 + -99960x + x2 = 2497999600 Factor a perfect square on the left side: (x + -49980)(x + -49980) = 2497999600 Calculate the square root of the right side: 49979.991996798 Break this problem into two subproblems by setting (x + -49980) equal to 49979.991996798 and -49979.991996798.Subproblem 1
x + -49980 = 49979.991996798 Simplifying x + -49980 = 49979.991996798 Reorder the terms: -49980 + x = 49979.991996798 Solving -49980 + x = 49979.991996798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49980' to each side of the equation. -49980 + 49980 + x = 49979.991996798 + 49980 Combine like terms: -49980 + 49980 = 0 0 + x = 49979.991996798 + 49980 x = 49979.991996798 + 49980 Combine like terms: 49979.991996798 + 49980 = 99959.991996798 x = 99959.991996798 Simplifying x = 99959.991996798Subproblem 2
x + -49980 = -49979.991996798 Simplifying x + -49980 = -49979.991996798 Reorder the terms: -49980 + x = -49979.991996798 Solving -49980 + x = -49979.991996798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '49980' to each side of the equation. -49980 + 49980 + x = -49979.991996798 + 49980 Combine like terms: -49980 + 49980 = 0 0 + x = -49979.991996798 + 49980 x = -49979.991996798 + 49980 Combine like terms: -49979.991996798 + 49980 = 0.008003202 x = 0.008003202 Simplifying x = 0.008003202Solution
The solution to the problem is based on the solutions from the subproblems. x = {99959.991996798, 0.008003202}
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