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Simplifying 0.02x2 + 162x + -16000 = 0 Reorder the terms: -16000 + 162x + 0.02x2 = 0 Solving -16000 + 162x + 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'. -800000 + 8100x + x2 = 0 Move the constant term to the right: Add '800000' to each side of the equation. -800000 + 8100x + 800000 + x2 = 0 + 800000 Reorder the terms: -800000 + 800000 + 8100x + x2 = 0 + 800000 Combine like terms: -800000 + 800000 = 0 0 + 8100x + x2 = 0 + 800000 8100x + x2 = 0 + 800000 Combine like terms: 0 + 800000 = 800000 8100x + x2 = 800000 The x term is 8100x. Take half its coefficient (4050). Square it (16402500) and add it to both sides. Add '16402500' to each side of the equation. 8100x + 16402500 + x2 = 800000 + 16402500 Reorder the terms: 16402500 + 8100x + x2 = 800000 + 16402500 Combine like terms: 800000 + 16402500 = 17202500 16402500 + 8100x + x2 = 17202500 Factor a perfect square on the left side: (x + 4050)(x + 4050) = 17202500 Calculate the square root of the right side: 4147.589661478 Break this problem into two subproblems by setting (x + 4050) equal to 4147.589661478 and -4147.589661478.Subproblem 1
x + 4050 = 4147.589661478 Simplifying x + 4050 = 4147.589661478 Reorder the terms: 4050 + x = 4147.589661478 Solving 4050 + x = 4147.589661478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4050' to each side of the equation. 4050 + -4050 + x = 4147.589661478 + -4050 Combine like terms: 4050 + -4050 = 0 0 + x = 4147.589661478 + -4050 x = 4147.589661478 + -4050 Combine like terms: 4147.589661478 + -4050 = 97.589661478 x = 97.589661478 Simplifying x = 97.589661478Subproblem 2
x + 4050 = -4147.589661478 Simplifying x + 4050 = -4147.589661478 Reorder the terms: 4050 + x = -4147.589661478 Solving 4050 + x = -4147.589661478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4050' to each side of the equation. 4050 + -4050 + x = -4147.589661478 + -4050 Combine like terms: 4050 + -4050 = 0 0 + x = -4147.589661478 + -4050 x = -4147.589661478 + -4050 Combine like terms: -4147.589661478 + -4050 = -8197.589661478 x = -8197.589661478 Simplifying x = -8197.589661478Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.589661478, -8197.589661478}
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