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Simplifying -0.1x2 + 142x + -3150 = 0 Reorder the terms: -3150 + 142x + -0.1x2 = 0 Solving -3150 + 142x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 31500 + -1420x + x2 = 0 Move the constant term to the right: Add '-31500' to each side of the equation. 31500 + -1420x + -31500 + x2 = 0 + -31500 Reorder the terms: 31500 + -31500 + -1420x + x2 = 0 + -31500 Combine like terms: 31500 + -31500 = 0 0 + -1420x + x2 = 0 + -31500 -1420x + x2 = 0 + -31500 Combine like terms: 0 + -31500 = -31500 -1420x + x2 = -31500 The x term is -1420x. Take half its coefficient (-710). Square it (504100) and add it to both sides. Add '504100' to each side of the equation. -1420x + 504100 + x2 = -31500 + 504100 Reorder the terms: 504100 + -1420x + x2 = -31500 + 504100 Combine like terms: -31500 + 504100 = 472600 504100 + -1420x + x2 = 472600 Factor a perfect square on the left side: (x + -710)(x + -710) = 472600 Calculate the square root of the right side: 687.459089692 Break this problem into two subproblems by setting (x + -710) equal to 687.459089692 and -687.459089692.Subproblem 1
x + -710 = 687.459089692 Simplifying x + -710 = 687.459089692 Reorder the terms: -710 + x = 687.459089692 Solving -710 + x = 687.459089692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '710' to each side of the equation. -710 + 710 + x = 687.459089692 + 710 Combine like terms: -710 + 710 = 0 0 + x = 687.459089692 + 710 x = 687.459089692 + 710 Combine like terms: 687.459089692 + 710 = 1397.459089692 x = 1397.459089692 Simplifying x = 1397.459089692Subproblem 2
x + -710 = -687.459089692 Simplifying x + -710 = -687.459089692 Reorder the terms: -710 + x = -687.459089692 Solving -710 + x = -687.459089692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '710' to each side of the equation. -710 + 710 + x = -687.459089692 + 710 Combine like terms: -710 + 710 = 0 0 + x = -687.459089692 + 710 x = -687.459089692 + 710 Combine like terms: -687.459089692 + 710 = 22.540910308 x = 22.540910308 Simplifying x = 22.540910308Solution
The solution to the problem is based on the solutions from the subproblems. x = {1397.459089692, 22.540910308}
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