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Simplifying -0.2x2 + 75x + -2000 = 0 Reorder the terms: -2000 + 75x + -0.2x2 = 0 Solving -2000 + 75x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 10000 + -375x + x2 = 0 Move the constant term to the right: Add '-10000' to each side of the equation. 10000 + -375x + -10000 + x2 = 0 + -10000 Reorder the terms: 10000 + -10000 + -375x + x2 = 0 + -10000 Combine like terms: 10000 + -10000 = 0 0 + -375x + x2 = 0 + -10000 -375x + x2 = 0 + -10000 Combine like terms: 0 + -10000 = -10000 -375x + x2 = -10000 The x term is -375x. Take half its coefficient (-187.5). Square it (35156.25) and add it to both sides. Add '35156.25' to each side of the equation. -375x + 35156.25 + x2 = -10000 + 35156.25 Reorder the terms: 35156.25 + -375x + x2 = -10000 + 35156.25 Combine like terms: -10000 + 35156.25 = 25156.25 35156.25 + -375x + x2 = 25156.25 Factor a perfect square on the left side: (x + -187.5)(x + -187.5) = 25156.25 Calculate the square root of the right side: 158.607219256 Break this problem into two subproblems by setting (x + -187.5) equal to 158.607219256 and -158.607219256.Subproblem 1
x + -187.5 = 158.607219256 Simplifying x + -187.5 = 158.607219256 Reorder the terms: -187.5 + x = 158.607219256 Solving -187.5 + x = 158.607219256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '187.5' to each side of the equation. -187.5 + 187.5 + x = 158.607219256 + 187.5 Combine like terms: -187.5 + 187.5 = 0.0 0.0 + x = 158.607219256 + 187.5 x = 158.607219256 + 187.5 Combine like terms: 158.607219256 + 187.5 = 346.107219256 x = 346.107219256 Simplifying x = 346.107219256Subproblem 2
x + -187.5 = -158.607219256 Simplifying x + -187.5 = -158.607219256 Reorder the terms: -187.5 + x = -158.607219256 Solving -187.5 + x = -158.607219256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '187.5' to each side of the equation. -187.5 + 187.5 + x = -158.607219256 + 187.5 Combine like terms: -187.5 + 187.5 = 0.0 0.0 + x = -158.607219256 + 187.5 x = -158.607219256 + 187.5 Combine like terms: -158.607219256 + 187.5 = 28.892780744 x = 28.892780744 Simplifying x = 28.892780744Solution
The solution to the problem is based on the solutions from the subproblems. x = {346.107219256, 28.892780744}
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