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Simplifying 0 = 2x2 + -3x + -1(3x + -1)(x + -2) Reorder the terms: 0 = 2x2 + -3x + -1(-1 + 3x)(x + -2) Reorder the terms: 0 = 2x2 + -3x + -1(-1 + 3x)(-2 + x) Multiply (-1 + 3x) * (-2 + x) 0 = 2x2 + -3x + -1(-1(-2 + x) + 3x * (-2 + x)) 0 = 2x2 + -3x + -1((-2 * -1 + x * -1) + 3x * (-2 + x)) 0 = 2x2 + -3x + -1((2 + -1x) + 3x * (-2 + x)) 0 = 2x2 + -3x + -1(2 + -1x + (-2 * 3x + x * 3x)) 0 = 2x2 + -3x + -1(2 + -1x + (-6x + 3x2)) Combine like terms: -1x + -6x = -7x 0 = 2x2 + -3x + -1(2 + -7x + 3x2) 0 = 2x2 + -3x + (2 * -1 + -7x * -1 + 3x2 * -1) 0 = 2x2 + -3x + (-2 + 7x + -3x2) Reorder the terms: 0 = -2 + -3x + 7x + 2x2 + -3x2 Combine like terms: -3x + 7x = 4x 0 = -2 + 4x + 2x2 + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 0 = -2 + 4x + -1x2 Solving 0 = -2 + 4x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + -4x + x2 = -2 + 4x + -1x2 + 2 + -4x + x2 Reorder the terms: 2 + -4x + x2 = -2 + 2 + 4x + -4x + -1x2 + x2 Combine like terms: -2 + 2 = 0 2 + -4x + x2 = 0 + 4x + -4x + -1x2 + x2 2 + -4x + x2 = 4x + -4x + -1x2 + x2 Combine like terms: 4x + -4x = 0 2 + -4x + x2 = 0 + -1x2 + x2 2 + -4x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 2 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4x + x2 = 0 + -2 -4x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4x + x2 = -2 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2 + 4 Reorder the terms: 4 + -4x + x2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + -4x + x2 = 2 Factor a perfect square on the left side: (x + -2)(x + -2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -2) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -2 = 1.414213562 Simplifying x + -2 = 1.414213562 Reorder the terms: -2 + x = 1.414213562 Solving -2 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.414213562 + 2 x = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 x = 3.414213562 Simplifying x = 3.414213562Subproblem 2
x + -2 = -1.414213562 Simplifying x + -2 = -1.414213562 Reorder the terms: -2 + x = -1.414213562 Solving -2 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.414213562 + 2 x = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 x = 0.585786438 Simplifying x = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.414213562, 0.585786438}
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