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Simplifying 0.19x = 2.5 + 0.15 + -0.0001x2 Combine like terms: 2.5 + 0.15 = 2.65 0.19x = 2.65 + -0.0001x2 Solving 0.19x = 2.65 + -0.0001x2 Solving for variable 'x'. Reorder the terms: -2.65 + 0.19x + 0.0001x2 = 2.65 + -0.0001x2 + -2.65 + 0.0001x2 Reorder the terms: -2.65 + 0.19x + 0.0001x2 = 2.65 + -2.65 + -0.0001x2 + 0.0001x2 Combine like terms: 2.65 + -2.65 = 0.00 -2.65 + 0.19x + 0.0001x2 = 0.00 + -0.0001x2 + 0.0001x2 -2.65 + 0.19x + 0.0001x2 = -0.0001x2 + 0.0001x2 Combine like terms: -0.0001x2 + 0.0001x2 = 0.0000 -2.65 + 0.19x + 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'. -26500 + 1900x + x2 = 0 Move the constant term to the right: Add '26500' to each side of the equation. -26500 + 1900x + 26500 + x2 = 0 + 26500 Reorder the terms: -26500 + 26500 + 1900x + x2 = 0 + 26500 Combine like terms: -26500 + 26500 = 0 0 + 1900x + x2 = 0 + 26500 1900x + x2 = 0 + 26500 Combine like terms: 0 + 26500 = 26500 1900x + x2 = 26500 The x term is 1900x. Take half its coefficient (950). Square it (902500) and add it to both sides. Add '902500' to each side of the equation. 1900x + 902500 + x2 = 26500 + 902500 Reorder the terms: 902500 + 1900x + x2 = 26500 + 902500 Combine like terms: 26500 + 902500 = 929000 902500 + 1900x + x2 = 929000 Factor a perfect square on the left side: (x + 950)(x + 950) = 929000 Calculate the square root of the right side: 963.846460802 Break this problem into two subproblems by setting (x + 950) equal to 963.846460802 and -963.846460802.Subproblem 1
x + 950 = 963.846460802 Simplifying x + 950 = 963.846460802 Reorder the terms: 950 + x = 963.846460802 Solving 950 + x = 963.846460802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-950' to each side of the equation. 950 + -950 + x = 963.846460802 + -950 Combine like terms: 950 + -950 = 0 0 + x = 963.846460802 + -950 x = 963.846460802 + -950 Combine like terms: 963.846460802 + -950 = 13.846460802 x = 13.846460802 Simplifying x = 13.846460802Subproblem 2
x + 950 = -963.846460802 Simplifying x + 950 = -963.846460802 Reorder the terms: 950 + x = -963.846460802 Solving 950 + x = -963.846460802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-950' to each side of the equation. 950 + -950 + x = -963.846460802 + -950 Combine like terms: 950 + -950 = 0 0 + x = -963.846460802 + -950 x = -963.846460802 + -950 Combine like terms: -963.846460802 + -950 = -1913.846460802 x = -1913.846460802 Simplifying x = -1913.846460802Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.846460802, -1913.846460802}
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