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Simplifying -0.02x2 + 102x + -10000 = 0 Reorder the terms: -10000 + 102x + -0.02x2 = 0 Solving -10000 + 102x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 500000 + -5100x + x2 = 0 Move the constant term to the right: Add '-500000' to each side of the equation. 500000 + -5100x + -500000 + x2 = 0 + -500000 Reorder the terms: 500000 + -500000 + -5100x + x2 = 0 + -500000 Combine like terms: 500000 + -500000 = 0 0 + -5100x + x2 = 0 + -500000 -5100x + x2 = 0 + -500000 Combine like terms: 0 + -500000 = -500000 -5100x + x2 = -500000 The x term is -5100x. Take half its coefficient (-2550). Square it (6502500) and add it to both sides. Add '6502500' to each side of the equation. -5100x + 6502500 + x2 = -500000 + 6502500 Reorder the terms: 6502500 + -5100x + x2 = -500000 + 6502500 Combine like terms: -500000 + 6502500 = 6002500 6502500 + -5100x + x2 = 6002500 Factor a perfect square on the left side: (x + -2550)(x + -2550) = 6002500 Calculate the square root of the right side: 2450 Break this problem into two subproblems by setting (x + -2550) equal to 2450 and -2450.Subproblem 1
x + -2550 = 2450 Simplifying x + -2550 = 2450 Reorder the terms: -2550 + x = 2450 Solving -2550 + x = 2450 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2550' to each side of the equation. -2550 + 2550 + x = 2450 + 2550 Combine like terms: -2550 + 2550 = 0 0 + x = 2450 + 2550 x = 2450 + 2550 Combine like terms: 2450 + 2550 = 5000 x = 5000 Simplifying x = 5000Subproblem 2
x + -2550 = -2450 Simplifying x + -2550 = -2450 Reorder the terms: -2550 + x = -2450 Solving -2550 + x = -2450 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2550' to each side of the equation. -2550 + 2550 + x = -2450 + 2550 Combine like terms: -2550 + 2550 = 0 0 + x = -2450 + 2550 x = -2450 + 2550 Combine like terms: -2450 + 2550 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {5000, 100}
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