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Simplifying 9x2 + -37x + 20 = 0 Reorder the terms: 20 + -37x + 9x2 = 0 Solving 20 + -37x + 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 + -4.111111111x + x2 = 0 Move the constant term to the right: Add '-2.222222222' to each side of the equation. 2.222222222 + -4.111111111x + -2.222222222 + x2 = 0 + -2.222222222 Reorder the terms: 2.222222222 + -2.222222222 + -4.111111111x + x2 = 0 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + -4.111111111x + x2 = 0 + -2.222222222 -4.111111111x + x2 = 0 + -2.222222222 Combine like terms: 0 + -2.222222222 = -2.222222222 -4.111111111x + x2 = -2.222222222 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 = -2.222222222 + 4.225308644 Reorder the terms: 4.225308644 + -4.111111111x + x2 = -2.222222222 + 4.225308644 Combine like terms: -2.222222222 + 4.225308644 = 2.003086422 4.225308644 + -4.111111111x + x2 = 2.003086422 Factor a perfect square on the left side: (x + -2.055555556)(x + -2.055555556) = 2.003086422 Calculate the square root of the right side: 1.415304357 Break this problem into two subproblems by setting (x + -2.055555556) equal to 1.415304357 and -1.415304357.Subproblem 1
x + -2.055555556 = 1.415304357 Simplifying x + -2.055555556 = 1.415304357 Reorder the terms: -2.055555556 + x = 1.415304357 Solving -2.055555556 + x = 1.415304357 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 = 1.415304357 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x = 1.415304357 + 2.055555556 x = 1.415304357 + 2.055555556 Combine like terms: 1.415304357 + 2.055555556 = 3.470859913 x = 3.470859913 Simplifying x = 3.470859913Subproblem 2
x + -2.055555556 = -1.415304357 Simplifying x + -2.055555556 = -1.415304357 Reorder the terms: -2.055555556 + x = -1.415304357 Solving -2.055555556 + x = -1.415304357 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 = -1.415304357 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x = -1.415304357 + 2.055555556 x = -1.415304357 + 2.055555556 Combine like terms: -1.415304357 + 2.055555556 = 0.640251199 x = 0.640251199 Simplifying x = 0.640251199Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.470859913, 0.640251199}
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