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Simplifying -0.2x2 + 176x + 21900 = 15000 Reorder the terms: 21900 + 176x + -0.2x2 = 15000 Solving 21900 + 176x + -0.2x2 = 15000 Solving for variable 'x'. Reorder the terms: 21900 + -15000 + 176x + -0.2x2 = 15000 + -15000 Combine like terms: 21900 + -15000 = 6900 6900 + 176x + -0.2x2 = 15000 + -15000 Combine like terms: 15000 + -15000 = 0 6900 + 176x + -0.2x2 = 0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -34500 + -880x + x2 = 0 Move the constant term to the right: Add '34500' to each side of the equation. -34500 + -880x + 34500 + x2 = 0 + 34500 Reorder the terms: -34500 + 34500 + -880x + x2 = 0 + 34500 Combine like terms: -34500 + 34500 = 0 0 + -880x + x2 = 0 + 34500 -880x + x2 = 0 + 34500 Combine like terms: 0 + 34500 = 34500 -880x + x2 = 34500 The x term is -880x. Take half its coefficient (-440). Square it (193600) and add it to both sides. Add '193600' to each side of the equation. -880x + 193600 + x2 = 34500 + 193600 Reorder the terms: 193600 + -880x + x2 = 34500 + 193600 Combine like terms: 34500 + 193600 = 228100 193600 + -880x + x2 = 228100 Factor a perfect square on the left side: (x + -440)(x + -440) = 228100 Calculate the square root of the right side: 477.59815745 Break this problem into two subproblems by setting (x + -440) equal to 477.59815745 and -477.59815745.Subproblem 1
x + -440 = 477.59815745 Simplifying x + -440 = 477.59815745 Reorder the terms: -440 + x = 477.59815745 Solving -440 + x = 477.59815745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '440' to each side of the equation. -440 + 440 + x = 477.59815745 + 440 Combine like terms: -440 + 440 = 0 0 + x = 477.59815745 + 440 x = 477.59815745 + 440 Combine like terms: 477.59815745 + 440 = 917.59815745 x = 917.59815745 Simplifying x = 917.59815745Subproblem 2
x + -440 = -477.59815745 Simplifying x + -440 = -477.59815745 Reorder the terms: -440 + x = -477.59815745 Solving -440 + x = -477.59815745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '440' to each side of the equation. -440 + 440 + x = -477.59815745 + 440 Combine like terms: -440 + 440 = 0 0 + x = -477.59815745 + 440 x = -477.59815745 + 440 Combine like terms: -477.59815745 + 440 = -37.59815745 x = -37.59815745 Simplifying x = -37.59815745Solution
The solution to the problem is based on the solutions from the subproblems. x = {917.59815745, -37.59815745}
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