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Simplifying 9x2 + 38x + 8 = x Reorder the terms: 8 + 38x + 9x2 = x Solving 8 + 38x + 9x2 = x Solving for variable 'x'. Reorder the terms: 8 + 38x + -1x + 9x2 = x + -1x Combine like terms: 38x + -1x = 37x 8 + 37x + 9x2 = x + -1x Combine like terms: x + -1x = 0 8 + 37x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 4.111111111x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 4.111111111x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 4.111111111x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 4.111111111x + x2 = 0 + -0.8888888889 4.111111111x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 4.111111111x + x2 = -0.8888888889 The x term is 4.111111111x. Take half its coefficient (2.055555556). Square it (4.225308644) and add it to both sides. Add '4.225308644' to each side of the equation. 4.111111111x + 4.225308644 + x2 = -0.8888888889 + 4.225308644 Reorder the terms: 4.225308644 + 4.111111111x + x2 = -0.8888888889 + 4.225308644 Combine like terms: -0.8888888889 + 4.225308644 = 3.3364197551 4.225308644 + 4.111111111x + x2 = 3.3364197551 Factor a perfect square on the left side: (x + 2.055555556)(x + 2.055555556) = 3.3364197551 Calculate the square root of the right side: 1.826586914 Break this problem into two subproblems by setting (x + 2.055555556) equal to 1.826586914 and -1.826586914.Subproblem 1
x + 2.055555556 = 1.826586914 Simplifying x + 2.055555556 = 1.826586914 Reorder the terms: 2.055555556 + x = 1.826586914 Solving 2.055555556 + x = 1.826586914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.055555556' to each side of the equation. 2.055555556 + -2.055555556 + x = 1.826586914 + -2.055555556 Combine like terms: 2.055555556 + -2.055555556 = 0.000000000 0.000000000 + x = 1.826586914 + -2.055555556 x = 1.826586914 + -2.055555556 Combine like terms: 1.826586914 + -2.055555556 = -0.228968642 x = -0.228968642 Simplifying x = -0.228968642Subproblem 2
x + 2.055555556 = -1.826586914 Simplifying x + 2.055555556 = -1.826586914 Reorder the terms: 2.055555556 + x = -1.826586914 Solving 2.055555556 + x = -1.826586914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.055555556' to each side of the equation. 2.055555556 + -2.055555556 + x = -1.826586914 + -2.055555556 Combine like terms: 2.055555556 + -2.055555556 = 0.000000000 0.000000000 + x = -1.826586914 + -2.055555556 x = -1.826586914 + -2.055555556 Combine like terms: -1.826586914 + -2.055555556 = -3.88214247 x = -3.88214247 Simplifying x = -3.88214247Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.228968642, -3.88214247}
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