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Simplifying 0.38 = x(1000000 + x) 0.38 = (1000000 * x + x * x) 0.38 = (1000000x + x2) Solving 0.38 = 1000000x + x2 Solving for variable 'x'. Reorder the terms: 0.38 + -1000000x + -1x2 = 1000000x + -1000000x + x2 + -1x2 Combine like terms: 1000000x + -1000000x = 0 0.38 + -1000000x + -1x2 = 0 + x2 + -1x2 0.38 + -1000000x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.38 + -1000000x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.38 + 1000000x + x2 = 0 Move the constant term to the right: Add '0.38' to each side of the equation. -0.38 + 1000000x + 0.38 + x2 = 0 + 0.38 Reorder the terms: -0.38 + 0.38 + 1000000x + x2 = 0 + 0.38 Combine like terms: -0.38 + 0.38 = 0.00 0.00 + 1000000x + x2 = 0 + 0.38 1000000x + x2 = 0 + 0.38 Combine like terms: 0 + 0.38 = 0.38 1000000x + x2 = 0.38 The x term is 1000000x. Take half its coefficient (500000). Square it (250000000000) and add it to both sides. Add '250000000000' to each side of the equation. 1000000x + 250000000000 + x2 = 0.38 + 250000000000 Reorder the terms: 250000000000 + 1000000x + x2 = 0.38 + 250000000000 Combine like terms: 0.38 + 250000000000 = 250000000000.38 250000000000 + 1000000x + x2 = 250000000000.38 Factor a perfect square on the left side: (x + 500000)(x + 500000) = 250000000000.38 Calculate the square root of the right side: 500000.00000038 Break this problem into two subproblems by setting (x + 500000) equal to 500000.00000038 and -500000.00000038.Subproblem 1
x + 500000 = 500000.00000038 Simplifying x + 500000 = 500000.00000038 Reorder the terms: 500000 + x = 500000.00000038 Solving 500000 + x = 500000.00000038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-500000' to each side of the equation. 500000 + -500000 + x = 500000.00000038 + -500000 Combine like terms: 500000 + -500000 = 0 0 + x = 500000.00000038 + -500000 x = 500000.00000038 + -500000 Combine like terms: 500000.00000038 + -500000 = 0.00000038 x = 0.00000038 Simplifying x = 0.00000038Subproblem 2
x + 500000 = -500000.00000038 Simplifying x + 500000 = -500000.00000038 Reorder the terms: 500000 + x = -500000.00000038 Solving 500000 + x = -500000.00000038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-500000' to each side of the equation. 500000 + -500000 + x = -500000.00000038 + -500000 Combine like terms: 500000 + -500000 = 0 0 + x = -500000.00000038 + -500000 x = -500000.00000038 + -500000 Combine like terms: -500000.00000038 + -500000 = -1000000.00000038 x = -1000000.00000038 Simplifying x = -1000000.00000038Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00000038, -1000000.00000038}
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