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Simplifying 9x2 + -19x + -29 = 0 Reorder the terms: -29 + -19x + 9x2 = 0 Solving -29 + -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'. -3.222222222 + -2.111111111x + x2 = 0 Move the constant term to the right: Add '3.222222222' to each side of the equation. -3.222222222 + -2.111111111x + 3.222222222 + x2 = 0 + 3.222222222 Reorder the terms: -3.222222222 + 3.222222222 + -2.111111111x + x2 = 0 + 3.222222222 Combine like terms: -3.222222222 + 3.222222222 = 0.000000000 0.000000000 + -2.111111111x + x2 = 0 + 3.222222222 -2.111111111x + x2 = 0 + 3.222222222 Combine like terms: 0 + 3.222222222 = 3.222222222 -2.111111111x + x2 = 3.222222222 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 = 3.222222222 + 1.114197532 Reorder the terms: 1.114197532 + -2.111111111x + x2 = 3.222222222 + 1.114197532 Combine like terms: 3.222222222 + 1.114197532 = 4.336419754 1.114197532 + -2.111111111x + x2 = 4.336419754 Factor a perfect square on the left side: (x + -1.055555556)(x + -1.055555556) = 4.336419754 Calculate the square root of the right side: 2.082407202 Break this problem into two subproblems by setting (x + -1.055555556) equal to 2.082407202 and -2.082407202.Subproblem 1
x + -1.055555556 = 2.082407202 Simplifying x + -1.055555556 = 2.082407202 Reorder the terms: -1.055555556 + x = 2.082407202 Solving -1.055555556 + x = 2.082407202 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 = 2.082407202 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = 2.082407202 + 1.055555556 x = 2.082407202 + 1.055555556 Combine like terms: 2.082407202 + 1.055555556 = 3.137962758 x = 3.137962758 Simplifying x = 3.137962758Subproblem 2
x + -1.055555556 = -2.082407202 Simplifying x + -1.055555556 = -2.082407202 Reorder the terms: -1.055555556 + x = -2.082407202 Solving -1.055555556 + x = -2.082407202 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 = -2.082407202 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = -2.082407202 + 1.055555556 x = -2.082407202 + 1.055555556 Combine like terms: -2.082407202 + 1.055555556 = -1.026851646 x = -1.026851646 Simplifying x = -1.026851646Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.137962758, -1.026851646}
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