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Simplifying 9x2 + -19x + -14 = 0 Reorder the terms: -14 + -19x + 9x2 = 0 Solving -14 + -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'. -1.555555556 + -2.111111111x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + -2.111111111x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + -2.111111111x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + -2.111111111x + x2 = 0 + 1.555555556 -2.111111111x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 -2.111111111x + x2 = 1.555555556 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 = 1.555555556 + 1.114197532 Reorder the terms: 1.114197532 + -2.111111111x + x2 = 1.555555556 + 1.114197532 Combine like terms: 1.555555556 + 1.114197532 = 2.669753088 1.114197532 + -2.111111111x + x2 = 2.669753088 Factor a perfect square on the left side: (x + -1.055555556)(x + -1.055555556) = 2.669753088 Calculate the square root of the right side: 1.633937908 Break this problem into two subproblems by setting (x + -1.055555556) equal to 1.633937908 and -1.633937908.Subproblem 1
x + -1.055555556 = 1.633937908 Simplifying x + -1.055555556 = 1.633937908 Reorder the terms: -1.055555556 + x = 1.633937908 Solving -1.055555556 + x = 1.633937908 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 = 1.633937908 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = 1.633937908 + 1.055555556 x = 1.633937908 + 1.055555556 Combine like terms: 1.633937908 + 1.055555556 = 2.689493464 x = 2.689493464 Simplifying x = 2.689493464Subproblem 2
x + -1.055555556 = -1.633937908 Simplifying x + -1.055555556 = -1.633937908 Reorder the terms: -1.055555556 + x = -1.633937908 Solving -1.055555556 + x = -1.633937908 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 = -1.633937908 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = -1.633937908 + 1.055555556 x = -1.633937908 + 1.055555556 Combine like terms: -1.633937908 + 1.055555556 = -0.578382352 x = -0.578382352 Simplifying x = -0.578382352Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.689493464, -0.578382352}
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