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Simplifying 800 = 100x + -0.5x2 Solving 800 = 100x + -0.5x2 Solving for variable 'x'. Reorder the terms: 800 + -100x + 0.5x2 = 100x + -100x + -0.5x2 + 0.5x2 Combine like terms: 100x + -100x = 0 800 + -100x + 0.5x2 = 0 + -0.5x2 + 0.5x2 800 + -100x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 800 + -100x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 1600 + -200x + x2 = 0 Move the constant term to the right: Add '-1600' to each side of the equation. 1600 + -200x + -1600 + x2 = 0 + -1600 Reorder the terms: 1600 + -1600 + -200x + x2 = 0 + -1600 Combine like terms: 1600 + -1600 = 0 0 + -200x + x2 = 0 + -1600 -200x + x2 = 0 + -1600 Combine like terms: 0 + -1600 = -1600 -200x + x2 = -1600 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -1600 + 10000 Reorder the terms: 10000 + -200x + x2 = -1600 + 10000 Combine like terms: -1600 + 10000 = 8400 10000 + -200x + x2 = 8400 Factor a perfect square on the left side: (x + -100)(x + -100) = 8400 Calculate the square root of the right side: 91.651513899 Break this problem into two subproblems by setting (x + -100) equal to 91.651513899 and -91.651513899.Subproblem 1
x + -100 = 91.651513899 Simplifying x + -100 = 91.651513899 Reorder the terms: -100 + x = 91.651513899 Solving -100 + x = 91.651513899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 91.651513899 + 100 Combine like terms: -100 + 100 = 0 0 + x = 91.651513899 + 100 x = 91.651513899 + 100 Combine like terms: 91.651513899 + 100 = 191.651513899 x = 191.651513899 Simplifying x = 191.651513899Subproblem 2
x + -100 = -91.651513899 Simplifying x + -100 = -91.651513899 Reorder the terms: -100 + x = -91.651513899 Solving -100 + x = -91.651513899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -91.651513899 + 100 Combine like terms: -100 + 100 = 0 0 + x = -91.651513899 + 100 x = -91.651513899 + 100 Combine like terms: -91.651513899 + 100 = 8.348486101 x = 8.348486101 Simplifying x = 8.348486101Solution
The solution to the problem is based on the solutions from the subproblems. x = {191.651513899, 8.348486101}
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