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Simplifying 276x2 + 0.94x + -0.055 = 0 Reorder the terms: -0.055 + 0.94x + 276x2 = 0 Solving -0.055 + 0.94x + 276x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 276 the coefficient of the squared term: Divide each side by '276'. -0.0001992753623 + 0.003405797101x + x2 = 0 Move the constant term to the right: Add '0.0001992753623' to each side of the equation. -0.0001992753623 + 0.003405797101x + 0.0001992753623 + x2 = 0 + 0.0001992753623 Reorder the terms: -0.0001992753623 + 0.0001992753623 + 0.003405797101x + x2 = 0 + 0.0001992753623 Combine like terms: -0.0001992753623 + 0.0001992753623 = 0.0000000000000 0.0000000000000 + 0.003405797101x + x2 = 0 + 0.0001992753623 0.003405797101x + x2 = 0 + 0.0001992753623 Combine like terms: 0 + 0.0001992753623 = 0.0001992753623 0.003405797101x + x2 = 0.0001992753623 The x term is 0.003405797101x. Take half its coefficient (0.001702898551). Square it (0.000002899863475) and add it to both sides. Add '0.000002899863475' to each side of the equation. 0.003405797101x + 0.000002899863475 + x2 = 0.0001992753623 + 0.000002899863475 Reorder the terms: 0.000002899863475 + 0.003405797101x + x2 = 0.0001992753623 + 0.000002899863475 Combine like terms: 0.0001992753623 + 0.000002899863475 = 0.000202175225775 0.000002899863475 + 0.003405797101x + x2 = 0.000202175225775 Factor a perfect square on the left side: (x + 0.001702898551)(x + 0.001702898551) = 0.000202175225775 Calculate the square root of the right side: 0.014218833 Break this problem into two subproblems by setting (x + 0.001702898551) equal to 0.014218833 and -0.014218833.Subproblem 1
x + 0.001702898551 = 0.014218833 Simplifying x + 0.001702898551 = 0.014218833 Reorder the terms: 0.001702898551 + x = 0.014218833 Solving 0.001702898551 + x = 0.014218833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.001702898551' to each side of the equation. 0.001702898551 + -0.001702898551 + x = 0.014218833 + -0.001702898551 Combine like terms: 0.001702898551 + -0.001702898551 = 0.000000000000 0.000000000000 + x = 0.014218833 + -0.001702898551 x = 0.014218833 + -0.001702898551 Combine like terms: 0.014218833 + -0.001702898551 = 0.012515934449 x = 0.012515934449 Simplifying x = 0.012515934449Subproblem 2
x + 0.001702898551 = -0.014218833 Simplifying x + 0.001702898551 = -0.014218833 Reorder the terms: 0.001702898551 + x = -0.014218833 Solving 0.001702898551 + x = -0.014218833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.001702898551' to each side of the equation. 0.001702898551 + -0.001702898551 + x = -0.014218833 + -0.001702898551 Combine like terms: 0.001702898551 + -0.001702898551 = 0.000000000000 0.000000000000 + x = -0.014218833 + -0.001702898551 x = -0.014218833 + -0.001702898551 Combine like terms: -0.014218833 + -0.001702898551 = -0.015921731551 x = -0.015921731551 Simplifying x = -0.015921731551Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.012515934449, -0.015921731551}
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