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Simplifying 75x = 3000 + 0.2x2 Solving 75x = 3000 + 0.2x2 Solving for variable 'x'. Reorder the terms: -3000 + 75x + -0.2x2 = 3000 + 0.2x2 + -3000 + -0.2x2 Reorder the terms: -3000 + 75x + -0.2x2 = 3000 + -3000 + 0.2x2 + -0.2x2 Combine like terms: 3000 + -3000 = 0 -3000 + 75x + -0.2x2 = 0 + 0.2x2 + -0.2x2 -3000 + 75x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 -3000 + 75x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 15000 + -375x + x2 = 0 Move the constant term to the right: Add '-15000' to each side of the equation. 15000 + -375x + -15000 + x2 = 0 + -15000 Reorder the terms: 15000 + -15000 + -375x + x2 = 0 + -15000 Combine like terms: 15000 + -15000 = 0 0 + -375x + x2 = 0 + -15000 -375x + x2 = 0 + -15000 Combine like terms: 0 + -15000 = -15000 -375x + x2 = -15000 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 = -15000 + 35156.25 Reorder the terms: 35156.25 + -375x + x2 = -15000 + 35156.25 Combine like terms: -15000 + 35156.25 = 20156.25 35156.25 + -375x + x2 = 20156.25 Factor a perfect square on the left side: (x + -187.5)(x + -187.5) = 20156.25 Calculate the square root of the right side: 141.972708645 Break this problem into two subproblems by setting (x + -187.5) equal to 141.972708645 and -141.972708645.Subproblem 1
x + -187.5 = 141.972708645 Simplifying x + -187.5 = 141.972708645 Reorder the terms: -187.5 + x = 141.972708645 Solving -187.5 + x = 141.972708645 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 = 141.972708645 + 187.5 Combine like terms: -187.5 + 187.5 = 0.0 0.0 + x = 141.972708645 + 187.5 x = 141.972708645 + 187.5 Combine like terms: 141.972708645 + 187.5 = 329.472708645 x = 329.472708645 Simplifying x = 329.472708645Subproblem 2
x + -187.5 = -141.972708645 Simplifying x + -187.5 = -141.972708645 Reorder the terms: -187.5 + x = -141.972708645 Solving -187.5 + x = -141.972708645 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 = -141.972708645 + 187.5 Combine like terms: -187.5 + 187.5 = 0.0 0.0 + x = -141.972708645 + 187.5 x = -141.972708645 + 187.5 Combine like terms: -141.972708645 + 187.5 = 45.527291355 x = 45.527291355 Simplifying x = 45.527291355Solution
The solution to the problem is based on the solutions from the subproblems. x = {329.472708645, 45.527291355}
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