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Simplifying 0.19x = 2.5 + 0.15x + -0.0001x2 Solving 0.19x = 2.5 + 0.15x + -0.0001x2 Solving for variable 'x'. Reorder the terms: -2.5 + 0.19x + -0.15x + 0.0001x2 = 2.5 + 0.15x + -0.0001x2 + -2.5 + -0.15x + 0.0001x2 Combine like terms: 0.19x + -0.15x = 0.04x -2.5 + 0.04x + 0.0001x2 = 2.5 + 0.15x + -0.0001x2 + -2.5 + -0.15x + 0.0001x2 Reorder the terms: -2.5 + 0.04x + 0.0001x2 = 2.5 + -2.5 + 0.15x + -0.15x + -0.0001x2 + 0.0001x2 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + 0.04x + 0.0001x2 = 0.0 + 0.15x + -0.15x + -0.0001x2 + 0.0001x2 -2.5 + 0.04x + 0.0001x2 = 0.15x + -0.15x + -0.0001x2 + 0.0001x2 Combine like terms: 0.15x + -0.15x = 0.00 -2.5 + 0.04x + 0.0001x2 = 0.00 + -0.0001x2 + 0.0001x2 -2.5 + 0.04x + 0.0001x2 = -0.0001x2 + 0.0001x2 Combine like terms: -0.0001x2 + 0.0001x2 = 0.0000 -2.5 + 0.04x + 0.0001x2 = 0.0000 Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. -25000 + 400x + x2 = 0 Move the constant term to the right: Add '25000' to each side of the equation. -25000 + 400x + 25000 + x2 = 0 + 25000 Reorder the terms: -25000 + 25000 + 400x + x2 = 0 + 25000 Combine like terms: -25000 + 25000 = 0 0 + 400x + x2 = 0 + 25000 400x + x2 = 0 + 25000 Combine like terms: 0 + 25000 = 25000 400x + x2 = 25000 The x term is 400x. Take half its coefficient (200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. 400x + 40000 + x2 = 25000 + 40000 Reorder the terms: 40000 + 400x + x2 = 25000 + 40000 Combine like terms: 25000 + 40000 = 65000 40000 + 400x + x2 = 65000 Factor a perfect square on the left side: (x + 200)(x + 200) = 65000 Calculate the square root of the right side: 254.95097568 Break this problem into two subproblems by setting (x + 200) equal to 254.95097568 and -254.95097568.Subproblem 1
x + 200 = 254.95097568 Simplifying x + 200 = 254.95097568 Reorder the terms: 200 + x = 254.95097568 Solving 200 + x = 254.95097568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = 254.95097568 + -200 Combine like terms: 200 + -200 = 0 0 + x = 254.95097568 + -200 x = 254.95097568 + -200 Combine like terms: 254.95097568 + -200 = 54.95097568 x = 54.95097568 Simplifying x = 54.95097568Subproblem 2
x + 200 = -254.95097568 Simplifying x + 200 = -254.95097568 Reorder the terms: 200 + x = -254.95097568 Solving 200 + x = -254.95097568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + x = -254.95097568 + -200 Combine like terms: 200 + -200 = 0 0 + x = -254.95097568 + -200 x = -254.95097568 + -200 Combine like terms: -254.95097568 + -200 = -454.95097568 x = -454.95097568 Simplifying x = -454.95097568Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.95097568, -454.95097568}
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