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Simplifying 0 = -9x2 + 600x + 50000 Reorder the terms: 0 = 50000 + 600x + -9x2 Solving 0 = 50000 + 600x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -50000 = -50000 -50000 + -600x + 9x2 = 50000 + 600x + -9x2 + -50000 + -600x + 9x2 Reorder the terms: -50000 + -600x + 9x2 = 50000 + -50000 + 600x + -600x + -9x2 + 9x2 Combine like terms: 50000 + -50000 = 0 -50000 + -600x + 9x2 = 0 + 600x + -600x + -9x2 + 9x2 -50000 + -600x + 9x2 = 600x + -600x + -9x2 + 9x2 Combine like terms: 600x + -600x = 0 -50000 + -600x + 9x2 = 0 + -9x2 + 9x2 -50000 + -600x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -50000 + -600x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5555.555556 + -66.66666667x + x2 = 0 Move the constant term to the right: Add '5555.555556' to each side of the equation. -5555.555556 + -66.66666667x + 5555.555556 + x2 = 0 + 5555.555556 Reorder the terms: -5555.555556 + 5555.555556 + -66.66666667x + x2 = 0 + 5555.555556 Combine like terms: -5555.555556 + 5555.555556 = 0.000000 0.000000 + -66.66666667x + x2 = 0 + 5555.555556 -66.66666667x + x2 = 0 + 5555.555556 Combine like terms: 0 + 5555.555556 = 5555.555556 -66.66666667x + x2 = 5555.555556 The x term is -66.66666667x. Take half its coefficient (-33.33333334). Square it (1111.111112) and add it to both sides. Add '1111.111112' to each side of the equation. -66.66666667x + 1111.111112 + x2 = 5555.555556 + 1111.111112 Reorder the terms: 1111.111112 + -66.66666667x + x2 = 5555.555556 + 1111.111112 Combine like terms: 5555.555556 + 1111.111112 = 6666.666668 1111.111112 + -66.66666667x + x2 = 6666.666668 Factor a perfect square on the left side: (x + -33.33333334)(x + -33.33333334) = 6666.666668 Calculate the square root of the right side: 81.649658101 Break this problem into two subproblems by setting (x + -33.33333334) equal to 81.649658101 and -81.649658101.Subproblem 1
x + -33.33333334 = 81.649658101 Simplifying x + -33.33333334 = 81.649658101 Reorder the terms: -33.33333334 + x = 81.649658101 Solving -33.33333334 + x = 81.649658101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = 81.649658101 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = 81.649658101 + 33.33333334 x = 81.649658101 + 33.33333334 Combine like terms: 81.649658101 + 33.33333334 = 114.982991441 x = 114.982991441 Simplifying x = 114.982991441Subproblem 2
x + -33.33333334 = -81.649658101 Simplifying x + -33.33333334 = -81.649658101 Reorder the terms: -33.33333334 + x = -81.649658101 Solving -33.33333334 + x = -81.649658101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = -81.649658101 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = -81.649658101 + 33.33333334 x = -81.649658101 + 33.33333334 Combine like terms: -81.649658101 + 33.33333334 = -48.316324761 x = -48.316324761 Simplifying x = -48.316324761Solution
The solution to the problem is based on the solutions from the subproblems. x = {114.982991441, -48.316324761}
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