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Simplifying 0 = 0.002x2 + 1.2x + 4 Reorder the terms: 0 = 4 + 1.2x + 0.002x2 Solving 0 = 4 + 1.2x + 0.002x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -1.2x + -0.002x2 = 4 + 1.2x + 0.002x2 + -4 + -1.2x + -0.002x2 Reorder the terms: -4 + -1.2x + -0.002x2 = 4 + -4 + 1.2x + -1.2x + 0.002x2 + -0.002x2 Combine like terms: 4 + -4 = 0 -4 + -1.2x + -0.002x2 = 0 + 1.2x + -1.2x + 0.002x2 + -0.002x2 -4 + -1.2x + -0.002x2 = 1.2x + -1.2x + 0.002x2 + -0.002x2 Combine like terms: 1.2x + -1.2x = 0.0 -4 + -1.2x + -0.002x2 = 0.0 + 0.002x2 + -0.002x2 -4 + -1.2x + -0.002x2 = 0.002x2 + -0.002x2 Combine like terms: 0.002x2 + -0.002x2 = 0.000 -4 + -1.2x + -0.002x2 = 0.000 Begin completing the square. Divide all terms by -0.002 the coefficient of the squared term: Divide each side by '-0.002'. 2000 + 600x + x2 = 0 Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + 600x + -2000 + x2 = 0 + -2000 Reorder the terms: 2000 + -2000 + 600x + x2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + 600x + x2 = 0 + -2000 600x + x2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 600x + x2 = -2000 The x term is 600x. Take half its coefficient (300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. 600x + 90000 + x2 = -2000 + 90000 Reorder the terms: 90000 + 600x + x2 = -2000 + 90000 Combine like terms: -2000 + 90000 = 88000 90000 + 600x + x2 = 88000 Factor a perfect square on the left side: (x + 300)(x + 300) = 88000 Calculate the square root of the right side: 296.647939484 Break this problem into two subproblems by setting (x + 300) equal to 296.647939484 and -296.647939484.Subproblem 1
x + 300 = 296.647939484 Simplifying x + 300 = 296.647939484 Reorder the terms: 300 + x = 296.647939484 Solving 300 + x = 296.647939484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 296.647939484 + -300 Combine like terms: 300 + -300 = 0 0 + x = 296.647939484 + -300 x = 296.647939484 + -300 Combine like terms: 296.647939484 + -300 = -3.352060516 x = -3.352060516 Simplifying x = -3.352060516Subproblem 2
x + 300 = -296.647939484 Simplifying x + 300 = -296.647939484 Reorder the terms: 300 + x = -296.647939484 Solving 300 + x = -296.647939484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -296.647939484 + -300 Combine like terms: 300 + -300 = 0 0 + x = -296.647939484 + -300 x = -296.647939484 + -300 Combine like terms: -296.647939484 + -300 = -596.647939484 x = -596.647939484 Simplifying x = -596.647939484Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.352060516, -596.647939484}
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