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Simplifying 0.08x2 + -160000x + -500000 = 0 Reorder the terms: -500000 + -160000x + 0.08x2 = 0 Solving -500000 + -160000x + 0.08x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. -6250000 + -2000000x + x2 = 0 Move the constant term to the right: Add '6250000' to each side of the equation. -6250000 + -2000000x + 6250000 + x2 = 0 + 6250000 Reorder the terms: -6250000 + 6250000 + -2000000x + x2 = 0 + 6250000 Combine like terms: -6250000 + 6250000 = 0 0 + -2000000x + x2 = 0 + 6250000 -2000000x + x2 = 0 + 6250000 Combine like terms: 0 + 6250000 = 6250000 -2000000x + x2 = 6250000 The x term is -2000000x. Take half its coefficient (-1000000). Square it (1000000000000) and add it to both sides. Add '1000000000000' to each side of the equation. -2000000x + 1000000000000 + x2 = 6250000 + 1000000000000 Reorder the terms: 1000000000000 + -2000000x + x2 = 6250000 + 1000000000000 Combine like terms: 6250000 + 1000000000000 = 1000006250000 1000000000000 + -2000000x + x2 = 1000006250000 Factor a perfect square on the left side: (x + -1000000)(x + -1000000) = 1000006250000 Calculate the square root of the right side: 1000003.124995117 Break this problem into two subproblems by setting (x + -1000000) equal to 1000003.124995117 and -1000003.124995117.Subproblem 1
x + -1000000 = 1000003.124995117 Simplifying x + -1000000 = 1000003.124995117 Reorder the terms: -1000000 + x = 1000003.124995117 Solving -1000000 + x = 1000003.124995117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000000' to each side of the equation. -1000000 + 1000000 + x = 1000003.124995117 + 1000000 Combine like terms: -1000000 + 1000000 = 0 0 + x = 1000003.124995117 + 1000000 x = 1000003.124995117 + 1000000 Combine like terms: 1000003.124995117 + 1000000 = 2000003.124995117 x = 2000003.124995117 Simplifying x = 2000003.124995117Subproblem 2
x + -1000000 = -1000003.124995117 Simplifying x + -1000000 = -1000003.124995117 Reorder the terms: -1000000 + x = -1000003.124995117 Solving -1000000 + x = -1000003.124995117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000000' to each side of the equation. -1000000 + 1000000 + x = -1000003.124995117 + 1000000 Combine like terms: -1000000 + 1000000 = 0 0 + x = -1000003.124995117 + 1000000 x = -1000003.124995117 + 1000000 Combine like terms: -1000003.124995117 + 1000000 = -3.124995117 x = -3.124995117 Simplifying x = -3.124995117Solution
The solution to the problem is based on the solutions from the subproblems. x = {2000003.124995117, -3.124995117}
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