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Simplifying -0.035x2 + 132x + -9570 = 0 Reorder the terms: -9570 + 132x + -0.035x2 = 0 Solving -9570 + 132x + -0.035x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.035 the coefficient of the squared term: Divide each side by '-0.035'. 273428.5714 + -3771.428571x + x2 = 0 Move the constant term to the right: Add '-273428.5714' to each side of the equation. 273428.5714 + -3771.428571x + -273428.5714 + x2 = 0 + -273428.5714 Reorder the terms: 273428.5714 + -273428.5714 + -3771.428571x + x2 = 0 + -273428.5714 Combine like terms: 273428.5714 + -273428.5714 = 0.0000 0.0000 + -3771.428571x + x2 = 0 + -273428.5714 -3771.428571x + x2 = 0 + -273428.5714 Combine like terms: 0 + -273428.5714 = -273428.5714 -3771.428571x + x2 = -273428.5714 The x term is -3771.428571x. Take half its coefficient (-1885.714286). Square it (3555918.368) and add it to both sides. Add '3555918.368' to each side of the equation. -3771.428571x + 3555918.368 + x2 = -273428.5714 + 3555918.368 Reorder the terms: 3555918.368 + -3771.428571x + x2 = -273428.5714 + 3555918.368 Combine like terms: -273428.5714 + 3555918.368 = 3282489.7966 3555918.368 + -3771.428571x + x2 = 3282489.7966 Factor a perfect square on the left side: (x + -1885.714286)(x + -1885.714286) = 3282489.7966 Calculate the square root of the right side: 1811.764277327 Break this problem into two subproblems by setting (x + -1885.714286) equal to 1811.764277327 and -1811.764277327.Subproblem 1
x + -1885.714286 = 1811.764277327 Simplifying x + -1885.714286 = 1811.764277327 Reorder the terms: -1885.714286 + x = 1811.764277327 Solving -1885.714286 + x = 1811.764277327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1885.714286' to each side of the equation. -1885.714286 + 1885.714286 + x = 1811.764277327 + 1885.714286 Combine like terms: -1885.714286 + 1885.714286 = 0.000000 0.000000 + x = 1811.764277327 + 1885.714286 x = 1811.764277327 + 1885.714286 Combine like terms: 1811.764277327 + 1885.714286 = 3697.478563327 x = 3697.478563327 Simplifying x = 3697.478563327Subproblem 2
x + -1885.714286 = -1811.764277327 Simplifying x + -1885.714286 = -1811.764277327 Reorder the terms: -1885.714286 + x = -1811.764277327 Solving -1885.714286 + x = -1811.764277327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1885.714286' to each side of the equation. -1885.714286 + 1885.714286 + x = -1811.764277327 + 1885.714286 Combine like terms: -1885.714286 + 1885.714286 = 0.000000 0.000000 + x = -1811.764277327 + 1885.714286 x = -1811.764277327 + 1885.714286 Combine like terms: -1811.764277327 + 1885.714286 = 73.950008673 x = 73.950008673 Simplifying x = 73.950008673Solution
The solution to the problem is based on the solutions from the subproblems. x = {3697.478563327, 73.950008673}
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