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Simplifying (x + -1)(x + -3) = 2(x + -2) Reorder the terms: (-1 + x)(x + -3) = 2(x + -2) Reorder the terms: (-1 + x)(-3 + x) = 2(x + -2) Multiply (-1 + x) * (-3 + x) (-1(-3 + x) + x(-3 + x)) = 2(x + -2) ((-3 * -1 + x * -1) + x(-3 + x)) = 2(x + -2) ((3 + -1x) + x(-3 + x)) = 2(x + -2) (3 + -1x + (-3 * x + x * x)) = 2(x + -2) (3 + -1x + (-3x + x2)) = 2(x + -2) Combine like terms: -1x + -3x = -4x (3 + -4x + x2) = 2(x + -2) Reorder the terms: 3 + -4x + x2 = 2(-2 + x) 3 + -4x + x2 = (-2 * 2 + x * 2) 3 + -4x + x2 = (-4 + 2x) Solving 3 + -4x + x2 = -4 + 2x Solving for variable 'x'. Reorder the terms: 3 + 4 + -4x + -2x + x2 = -4 + 2x + 4 + -2x Combine like terms: 3 + 4 = 7 7 + -4x + -2x + x2 = -4 + 2x + 4 + -2x Combine like terms: -4x + -2x = -6x 7 + -6x + x2 = -4 + 2x + 4 + -2x Reorder the terms: 7 + -6x + x2 = -4 + 4 + 2x + -2x Combine like terms: -4 + 4 = 0 7 + -6x + x2 = 0 + 2x + -2x 7 + -6x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 7 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -6x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x + x2 = 0 + -7 -6x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6x + x2 = -7 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -7 + 9 Reorder the terms: 9 + -6x + x2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6x + x2 = 2 Factor a perfect square on the left side: (x + -3)(x + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -3 = 1.414213562 Simplifying x + -3 = 1.414213562 Reorder the terms: -3 + x = 1.414213562 Solving -3 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.414213562 + 3 x = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 x = 4.414213562 Simplifying x = 4.414213562Subproblem 2
x + -3 = -1.414213562 Simplifying x + -3 = -1.414213562 Reorder the terms: -3 + x = -1.414213562 Solving -3 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.414213562 + 3 x = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 x = 1.585786438 Simplifying x = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.414213562, 1.585786438}
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