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Simplifying 0 = 0.002x2 + 0.3x + -50 Reorder the terms: 0 = -50 + 0.3x + 0.002x2 Solving 0 = -50 + 0.3x + 0.002x2 Solving for variable 'x'. Combine like terms: 0 + 50 = 50 50 + -0.3x + -0.002x2 = -50 + 0.3x + 0.002x2 + 50 + -0.3x + -0.002x2 Reorder the terms: 50 + -0.3x + -0.002x2 = -50 + 50 + 0.3x + -0.3x + 0.002x2 + -0.002x2 Combine like terms: -50 + 50 = 0 50 + -0.3x + -0.002x2 = 0 + 0.3x + -0.3x + 0.002x2 + -0.002x2 50 + -0.3x + -0.002x2 = 0.3x + -0.3x + 0.002x2 + -0.002x2 Combine like terms: 0.3x + -0.3x = 0.0 50 + -0.3x + -0.002x2 = 0.0 + 0.002x2 + -0.002x2 50 + -0.3x + -0.002x2 = 0.002x2 + -0.002x2 Combine like terms: 0.002x2 + -0.002x2 = 0.000 50 + -0.3x + -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'. -25000 + 150x + x2 = 0 Move the constant term to the right: Add '25000' to each side of the equation. -25000 + 150x + 25000 + x2 = 0 + 25000 Reorder the terms: -25000 + 25000 + 150x + x2 = 0 + 25000 Combine like terms: -25000 + 25000 = 0 0 + 150x + x2 = 0 + 25000 150x + x2 = 0 + 25000 Combine like terms: 0 + 25000 = 25000 150x + x2 = 25000 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = 25000 + 5625 Reorder the terms: 5625 + 150x + x2 = 25000 + 5625 Combine like terms: 25000 + 5625 = 30625 5625 + 150x + x2 = 30625 Factor a perfect square on the left side: (x + 75)(x + 75) = 30625 Calculate the square root of the right side: 175 Break this problem into two subproblems by setting (x + 75) equal to 175 and -175.Subproblem 1
x + 75 = 175 Simplifying x + 75 = 175 Reorder the terms: 75 + x = 175 Solving 75 + x = 175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 175 + -75 Combine like terms: 75 + -75 = 0 0 + x = 175 + -75 x = 175 + -75 Combine like terms: 175 + -75 = 100 x = 100 Simplifying x = 100Subproblem 2
x + 75 = -175 Simplifying x + 75 = -175 Reorder the terms: 75 + x = -175 Solving 75 + x = -175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -175 + -75 Combine like terms: 75 + -75 = 0 0 + x = -175 + -75 x = -175 + -75 Combine like terms: -175 + -75 = -250 x = -250 Simplifying x = -250Solution
The solution to the problem is based on the solutions from the subproblems. x = {100, -250}
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