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Simplifying 0.5x2 + -75x = -937.5 Reorder the terms: -75x + 0.5x2 = -937.5 Solving -75x + 0.5x2 = -937.5 Solving for variable 'x'. Reorder the terms: 937.5 + -75x + 0.5x2 = -937.5 + 937.5 Combine like terms: -937.5 + 937.5 = 0.0 937.5 + -75x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 1875 + -150x + x2 = 0 Move the constant term to the right: Add '-1875' to each side of the equation. 1875 + -150x + -1875 + x2 = 0 + -1875 Reorder the terms: 1875 + -1875 + -150x + x2 = 0 + -1875 Combine like terms: 1875 + -1875 = 0 0 + -150x + x2 = 0 + -1875 -150x + x2 = 0 + -1875 Combine like terms: 0 + -1875 = -1875 -150x + x2 = -1875 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 = -1875 + 5625 Reorder the terms: 5625 + -150x + x2 = -1875 + 5625 Combine like terms: -1875 + 5625 = 3750 5625 + -150x + x2 = 3750 Factor a perfect square on the left side: (x + -75)(x + -75) = 3750 Calculate the square root of the right side: 61.23724357 Break this problem into two subproblems by setting (x + -75) equal to 61.23724357 and -61.23724357.Subproblem 1
x + -75 = 61.23724357 Simplifying x + -75 = 61.23724357 Reorder the terms: -75 + x = 61.23724357 Solving -75 + x = 61.23724357 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 = 61.23724357 + 75 Combine like terms: -75 + 75 = 0 0 + x = 61.23724357 + 75 x = 61.23724357 + 75 Combine like terms: 61.23724357 + 75 = 136.23724357 x = 136.23724357 Simplifying x = 136.23724357Subproblem 2
x + -75 = -61.23724357 Simplifying x + -75 = -61.23724357 Reorder the terms: -75 + x = -61.23724357 Solving -75 + x = -61.23724357 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 = -61.23724357 + 75 Combine like terms: -75 + 75 = 0 0 + x = -61.23724357 + 75 x = -61.23724357 + 75 Combine like terms: -61.23724357 + 75 = 13.76275643 x = 13.76275643 Simplifying x = 13.76275643Solution
The solution to the problem is based on the solutions from the subproblems. x = {136.23724357, 13.76275643}
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