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Simplifying -0.002x2 + -0.5x + 10 = 0 Reorder the terms: 10 + -0.5x + -0.002x2 = 0 Solving 10 + -0.5x + -0.002x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.002 the coefficient of the squared term: Divide each side by '-0.002'. -5000 + 250x + x2 = 0 Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 250x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 250x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 250x + x2 = 0 + 5000 250x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 250x + x2 = 5000 The x term is 250x. Take half its coefficient (125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. 250x + 15625 + x2 = 5000 + 15625 Reorder the terms: 15625 + 250x + x2 = 5000 + 15625 Combine like terms: 5000 + 15625 = 20625 15625 + 250x + x2 = 20625 Factor a perfect square on the left side: (x + 125)(x + 125) = 20625 Calculate the square root of the right side: 143.614066163 Break this problem into two subproblems by setting (x + 125) equal to 143.614066163 and -143.614066163.Subproblem 1
x + 125 = 143.614066163 Simplifying x + 125 = 143.614066163 Reorder the terms: 125 + x = 143.614066163 Solving 125 + x = 143.614066163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = 143.614066163 + -125 Combine like terms: 125 + -125 = 0 0 + x = 143.614066163 + -125 x = 143.614066163 + -125 Combine like terms: 143.614066163 + -125 = 18.614066163 x = 18.614066163 Simplifying x = 18.614066163Subproblem 2
x + 125 = -143.614066163 Simplifying x + 125 = -143.614066163 Reorder the terms: 125 + x = -143.614066163 Solving 125 + x = -143.614066163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + x = -143.614066163 + -125 Combine like terms: 125 + -125 = 0 0 + x = -143.614066163 + -125 x = -143.614066163 + -125 Combine like terms: -143.614066163 + -125 = -268.614066163 x = -268.614066163 Simplifying x = -268.614066163Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.614066163, -268.614066163}
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