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Simplifying -0.05x + -0.0002x2 = -18 Solving -0.05x + -0.0002x2 = -18 Solving for variable 'x'. Reorder the terms: 18 + -0.05x + -0.0002x2 = -18 + 18 Combine like terms: -18 + 18 = 0 18 + -0.05x + -0.0002x2 = 0 Begin completing the square. Divide all terms by -0.0002 the coefficient of the squared term: Divide each side by '-0.0002'. -90000 + 250x + x2 = 0 Move the constant term to the right: Add '90000' to each side of the equation. -90000 + 250x + 90000 + x2 = 0 + 90000 Reorder the terms: -90000 + 90000 + 250x + x2 = 0 + 90000 Combine like terms: -90000 + 90000 = 0 0 + 250x + x2 = 0 + 90000 250x + x2 = 0 + 90000 Combine like terms: 0 + 90000 = 90000 250x + x2 = 90000 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 = 90000 + 15625 Reorder the terms: 15625 + 250x + x2 = 90000 + 15625 Combine like terms: 90000 + 15625 = 105625 15625 + 250x + x2 = 105625 Factor a perfect square on the left side: (x + 125)(x + 125) = 105625 Calculate the square root of the right side: 325 Break this problem into two subproblems by setting (x + 125) equal to 325 and -325.Subproblem 1
x + 125 = 325 Simplifying x + 125 = 325 Reorder the terms: 125 + x = 325 Solving 125 + x = 325 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 = 325 + -125 Combine like terms: 125 + -125 = 0 0 + x = 325 + -125 x = 325 + -125 Combine like terms: 325 + -125 = 200 x = 200 Simplifying x = 200Subproblem 2
x + 125 = -325 Simplifying x + 125 = -325 Reorder the terms: 125 + x = -325 Solving 125 + x = -325 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 = -325 + -125 Combine like terms: 125 + -125 = 0 0 + x = -325 + -125 x = -325 + -125 Combine like terms: -325 + -125 = -450 x = -450 Simplifying x = -450Solution
The solution to the problem is based on the solutions from the subproblems. x = {200, -450}
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