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Simplifying 9x2 + 19x + -20 = 0 Reorder the terms: -20 + 19x + 9x2 = 0 Solving -20 + 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'. -2.222222222 + 2.111111111x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 2.111111111x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 2.111111111x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 2.111111111x + x2 = 0 + 2.222222222 2.111111111x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 2.111111111x + x2 = 2.222222222 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 = 2.222222222 + 1.114197532 Reorder the terms: 1.114197532 + 2.111111111x + x2 = 2.222222222 + 1.114197532 Combine like terms: 2.222222222 + 1.114197532 = 3.336419754 1.114197532 + 2.111111111x + x2 = 3.336419754 Factor a perfect square on the left side: (x + 1.055555556)(x + 1.055555556) = 3.336419754 Calculate the square root of the right side: 1.826586914 Break this problem into two subproblems by setting (x + 1.055555556) equal to 1.826586914 and -1.826586914.Subproblem 1
x + 1.055555556 = 1.826586914 Simplifying x + 1.055555556 = 1.826586914 Reorder the terms: 1.055555556 + x = 1.826586914 Solving 1.055555556 + x = 1.826586914 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 = 1.826586914 + -1.055555556 Combine like terms: 1.055555556 + -1.055555556 = 0.000000000 0.000000000 + x = 1.826586914 + -1.055555556 x = 1.826586914 + -1.055555556 Combine like terms: 1.826586914 + -1.055555556 = 0.771031358 x = 0.771031358 Simplifying x = 0.771031358Subproblem 2
x + 1.055555556 = -1.826586914 Simplifying x + 1.055555556 = -1.826586914 Reorder the terms: 1.055555556 + x = -1.826586914 Solving 1.055555556 + x = -1.826586914 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 = -1.826586914 + -1.055555556 Combine like terms: 1.055555556 + -1.055555556 = 0.000000000 0.000000000 + x = -1.826586914 + -1.055555556 x = -1.826586914 + -1.055555556 Combine like terms: -1.826586914 + -1.055555556 = -2.88214247 x = -2.88214247 Simplifying x = -2.88214247Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.771031358, -2.88214247}
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