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Simplifying 9x2 + 19x + -6 = 0 Reorder the terms: -6 + 19x + 9x2 = 0 Solving -6 + 19x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.6666666667 + 2.111111111x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2.111111111x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2.111111111x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2.111111111x + x2 = 0 + 0.6666666667 2.111111111x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2.111111111x + x2 = 0.6666666667 The x term is 2.111111111x. Take half its coefficient (1.055555556). Square it (1.114197532) and add it to both sides. Add '1.114197532' to each side of the equation. 2.111111111x + 1.114197532 + x2 = 0.6666666667 + 1.114197532 Reorder the terms: 1.114197532 + 2.111111111x + x2 = 0.6666666667 + 1.114197532 Combine like terms: 0.6666666667 + 1.114197532 = 1.7808641987 1.114197532 + 2.111111111x + x2 = 1.7808641987 Factor a perfect square on the left side: (x + 1.055555556)(x + 1.055555556) = 1.7808641987 Calculate the square root of the right side: 1.334490239 Break this problem into two subproblems by setting (x + 1.055555556) equal to 1.334490239 and -1.334490239.Subproblem 1
x + 1.055555556 = 1.334490239 Simplifying x + 1.055555556 = 1.334490239 Reorder the terms: 1.055555556 + x = 1.334490239 Solving 1.055555556 + x = 1.334490239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.055555556' to each side of the equation. 1.055555556 + -1.055555556 + x = 1.334490239 + -1.055555556 Combine like terms: 1.055555556 + -1.055555556 = 0.000000000 0.000000000 + x = 1.334490239 + -1.055555556 x = 1.334490239 + -1.055555556 Combine like terms: 1.334490239 + -1.055555556 = 0.278934683 x = 0.278934683 Simplifying x = 0.278934683Subproblem 2
x + 1.055555556 = -1.334490239 Simplifying x + 1.055555556 = -1.334490239 Reorder the terms: 1.055555556 + x = -1.334490239 Solving 1.055555556 + x = -1.334490239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.055555556' to each side of the equation. 1.055555556 + -1.055555556 + x = -1.334490239 + -1.055555556 Combine like terms: 1.055555556 + -1.055555556 = 0.000000000 0.000000000 + x = -1.334490239 + -1.055555556 x = -1.334490239 + -1.055555556 Combine like terms: -1.334490239 + -1.055555556 = -2.390045795 x = -2.390045795 Simplifying x = -2.390045795Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.278934683, -2.390045795}
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