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Simplifying 0.02 = x(11000000 + x) 0.02 = (11000000 * x + x * x) 0.02 = (11000000x + x2) Solving 0.02 = 11000000x + x2 Solving for variable 'x'. Reorder the terms: 0.02 + -11000000x + -1x2 = 11000000x + -11000000x + x2 + -1x2 Combine like terms: 11000000x + -11000000x = 0 0.02 + -11000000x + -1x2 = 0 + x2 + -1x2 0.02 + -11000000x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.02 + -11000000x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.02 + 11000000x + x2 = 0 Move the constant term to the right: Add '0.02' to each side of the equation. -0.02 + 11000000x + 0.02 + x2 = 0 + 0.02 Reorder the terms: -0.02 + 0.02 + 11000000x + x2 = 0 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + 11000000x + x2 = 0 + 0.02 11000000x + x2 = 0 + 0.02 Combine like terms: 0 + 0.02 = 0.02 11000000x + x2 = 0.02 The x term is 11000000x. Take half its coefficient (5500000). Square it (30250000000000) and add it to both sides. Add '30250000000000' to each side of the equation. 11000000x + 30250000000000 + x2 = 0.02 + 30250000000000 Reorder the terms: 30250000000000 + 11000000x + x2 = 0.02 + 30250000000000 Combine like terms: 0.02 + 30250000000000 = 30250000000000.02 30250000000000 + 11000000x + x2 = 30250000000000.02 Factor a perfect square on the left side: (x + 5500000)(x + 5500000) = 30250000000000.02 Calculate the square root of the right side: 5500000.000000002 Break this problem into two subproblems by setting (x + 5500000) equal to 5500000.000000002 and -5500000.000000002.Subproblem 1
x + 5500000 = 5500000.000000002 Simplifying x + 5500000 = 5500000.000000002 Reorder the terms: 5500000 + x = 5500000.000000002 Solving 5500000 + x = 5500000.000000002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5500000' to each side of the equation. 5500000 + -5500000 + x = 5500000.000000002 + -5500000 Combine like terms: 5500000 + -5500000 = 0 0 + x = 5500000.000000002 + -5500000 x = 5500000.000000002 + -5500000 Combine like terms: 5500000.000000002 + -5500000 = 0.000000002 x = 0.000000002 Simplifying x = 0.000000002Subproblem 2
x + 5500000 = -5500000.000000002 Simplifying x + 5500000 = -5500000.000000002 Reorder the terms: 5500000 + x = -5500000.000000002 Solving 5500000 + x = -5500000.000000002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5500000' to each side of the equation. 5500000 + -5500000 + x = -5500000.000000002 + -5500000 Combine like terms: 5500000 + -5500000 = 0 0 + x = -5500000.000000002 + -5500000 x = -5500000.000000002 + -5500000 Combine like terms: -5500000.000000002 + -5500000 = -11000000.000000002 x = -11000000.000000002 Simplifying x = -11000000.000000002Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000000002, -11000000.000000002}
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