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Simplifying 45x + -0.025x2 + -5000 = 0 Reorder the terms: -5000 + 45x + -0.025x2 = 0 Solving -5000 + 45x + -0.025x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.025 the coefficient of the squared term: Divide each side by '-0.025'. 200000 + -1800x + x2 = 0 Move the constant term to the right: Add '-200000' to each side of the equation. 200000 + -1800x + -200000 + x2 = 0 + -200000 Reorder the terms: 200000 + -200000 + -1800x + x2 = 0 + -200000 Combine like terms: 200000 + -200000 = 0 0 + -1800x + x2 = 0 + -200000 -1800x + x2 = 0 + -200000 Combine like terms: 0 + -200000 = -200000 -1800x + x2 = -200000 The x term is -1800x. Take half its coefficient (-900). Square it (810000) and add it to both sides. Add '810000' to each side of the equation. -1800x + 810000 + x2 = -200000 + 810000 Reorder the terms: 810000 + -1800x + x2 = -200000 + 810000 Combine like terms: -200000 + 810000 = 610000 810000 + -1800x + x2 = 610000 Factor a perfect square on the left side: (x + -900)(x + -900) = 610000 Calculate the square root of the right side: 781.024967591 Break this problem into two subproblems by setting (x + -900) equal to 781.024967591 and -781.024967591.Subproblem 1
x + -900 = 781.024967591 Simplifying x + -900 = 781.024967591 Reorder the terms: -900 + x = 781.024967591 Solving -900 + x = 781.024967591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '900' to each side of the equation. -900 + 900 + x = 781.024967591 + 900 Combine like terms: -900 + 900 = 0 0 + x = 781.024967591 + 900 x = 781.024967591 + 900 Combine like terms: 781.024967591 + 900 = 1681.024967591 x = 1681.024967591 Simplifying x = 1681.024967591Subproblem 2
x + -900 = -781.024967591 Simplifying x + -900 = -781.024967591 Reorder the terms: -900 + x = -781.024967591 Solving -900 + x = -781.024967591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '900' to each side of the equation. -900 + 900 + x = -781.024967591 + 900 Combine like terms: -900 + 900 = 0 0 + x = -781.024967591 + 900 x = -781.024967591 + 900 Combine like terms: -781.024967591 + 900 = 118.975032409 x = 118.975032409 Simplifying x = 118.975032409Solution
The solution to the problem is based on the solutions from the subproblems. x = {1681.024967591, 118.975032409}
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