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Simplifying 0.999x2 + 0.0001352x + -0.00000330 = 0 Reorder the terms: -0.00000330 + 0.0001352x + 0.999x2 = 0 Solving -0.00000330 + 0.0001352x + 0.999x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.999 the coefficient of the squared term: Divide each side by '0.999'. -0.000003303303303 + 0.0001353353353x + x2 = 0 Move the constant term to the right: Add '0.000003303303303' to each side of the equation. -0.000003303303303 + 0.0001353353353x + 0.000003303303303 + x2 = 0 + 0.000003303303303 Reorder the terms: -0.000003303303303 + 0.000003303303303 + 0.0001353353353x + x2 = 0 + 0.000003303303303 Combine like terms: -0.000003303303303 + 0.000003303303303 = 0.000000000000000 0.000000000000000 + 0.0001353353353x + x2 = 0 + 0.000003303303303 0.0001353353353x + x2 = 0 + 0.000003303303303 Combine like terms: 0 + 0.000003303303303 = 0.000003303303303 0.0001353353353x + x2 = 0.000003303303303 The x term is 0.0001353353353x. Take half its coefficient (0.00006766766765). Square it (0.000000004578913245) and add it to both sides. Add '0.000000004578913245' to each side of the equation. 0.0001353353353x + 0.000000004578913245 + x2 = 0.000003303303303 + 0.000000004578913245 Reorder the terms: 0.000000004578913245 + 0.0001353353353x + x2 = 0.000003303303303 + 0.000000004578913245 Combine like terms: 0.000003303303303 + 0.000000004578913245 = 0.000003307882216245 0.000000004578913245 + 0.0001353353353x + x2 = 0.000003307882216245 Factor a perfect square on the left side: (x + 0.00006766766765)(x + 0.00006766766765) = 0.000003307882216245 Calculate the square root of the right side: 0.001818758 Break this problem into two subproblems by setting (x + 0.00006766766765) equal to 0.001818758 and -0.001818758.Subproblem 1
x + 0.00006766766765 = 0.001818758 Simplifying x + 0.00006766766765 = 0.001818758 Reorder the terms: 0.00006766766765 + x = 0.001818758 Solving 0.00006766766765 + x = 0.001818758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00006766766765' to each side of the equation. 0.00006766766765 + -0.00006766766765 + x = 0.001818758 + -0.00006766766765 Combine like terms: 0.00006766766765 + -0.00006766766765 = 0.00000000000000 0.00000000000000 + x = 0.001818758 + -0.00006766766765 x = 0.001818758 + -0.00006766766765 Combine like terms: 0.001818758 + -0.00006766766765 = 0.00175109033235 x = 0.00175109033235 Simplifying x = 0.00175109033235Subproblem 2
x + 0.00006766766765 = -0.001818758 Simplifying x + 0.00006766766765 = -0.001818758 Reorder the terms: 0.00006766766765 + x = -0.001818758 Solving 0.00006766766765 + x = -0.001818758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00006766766765' to each side of the equation. 0.00006766766765 + -0.00006766766765 + x = -0.001818758 + -0.00006766766765 Combine like terms: 0.00006766766765 + -0.00006766766765 = 0.00000000000000 0.00000000000000 + x = -0.001818758 + -0.00006766766765 x = -0.001818758 + -0.00006766766765 Combine like terms: -0.001818758 + -0.00006766766765 = -0.00188642566765 x = -0.00188642566765 Simplifying x = -0.00188642566765Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00175109033235, -0.00188642566765}
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