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Simplifying (x + -1)(x + -1) + -1(x * x + -4) + -2(x + 1)(x + 1) = 0 Reorder the terms: (-1 + x)(x + -1) + -1(x * x + -4) + -2(x + 1)(x + 1) = 0 Reorder the terms: (-1 + x)(-1 + x) + -1(x * x + -4) + -2(x + 1)(x + 1) = 0 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x)) + -1(x * x + -4) + -2(x + 1)(x + 1) = 0 ((-1 * -1 + x * -1) + x(-1 + x)) + -1(x * x + -4) + -2(x + 1)(x + 1) = 0 ((1 + -1x) + x(-1 + x)) + -1(x * x + -4) + -2(x + 1)(x + 1) = 0 (1 + -1x + (-1 * x + x * x)) + -1(x * x + -4) + -2(x + 1)(x + 1) = 0 (1 + -1x + (-1x + x2)) + -1(x * x + -4) + -2(x + 1)(x + 1) = 0 Combine like terms: -1x + -1x = -2x (1 + -2x + x2) + -1(x * x + -4) + -2(x + 1)(x + 1) = 0 Multiply x * x 1 + -2x + x2 + -1(x2 + -4) + -2(x + 1)(x + 1) = 0 Reorder the terms: 1 + -2x + x2 + -1(-4 + x2) + -2(x + 1)(x + 1) = 0 1 + -2x + x2 + (-4 * -1 + x2 * -1) + -2(x + 1)(x + 1) = 0 1 + -2x + x2 + (4 + -1x2) + -2(x + 1)(x + 1) = 0 Reorder the terms: 1 + -2x + x2 + 4 + -1x2 + -2(1 + x)(x + 1) = 0 Reorder the terms: 1 + -2x + x2 + 4 + -1x2 + -2(1 + x)(1 + x) = 0 Multiply (1 + x) * (1 + x) 1 + -2x + x2 + 4 + -1x2 + -2(1(1 + x) + x(1 + x)) = 0 1 + -2x + x2 + 4 + -1x2 + -2((1 * 1 + x * 1) + x(1 + x)) = 0 1 + -2x + x2 + 4 + -1x2 + -2((1 + 1x) + x(1 + x)) = 0 1 + -2x + x2 + 4 + -1x2 + -2(1 + 1x + (1 * x + x * x)) = 0 1 + -2x + x2 + 4 + -1x2 + -2(1 + 1x + (1x + x2)) = 0 Combine like terms: 1x + 1x = 2x 1 + -2x + x2 + 4 + -1x2 + -2(1 + 2x + x2) = 0 1 + -2x + x2 + 4 + -1x2 + (1 * -2 + 2x * -2 + x2 * -2) = 0 1 + -2x + x2 + 4 + -1x2 + (-2 + -4x + -2x2) = 0 Reorder the terms: 1 + 4 + -2 + -2x + -4x + x2 + -1x2 + -2x2 = 0 Combine like terms: 1 + 4 = 5 5 + -2 + -2x + -4x + x2 + -1x2 + -2x2 = 0 Combine like terms: 5 + -2 = 3 3 + -2x + -4x + x2 + -1x2 + -2x2 = 0 Combine like terms: -2x + -4x = -6x 3 + -6x + x2 + -1x2 + -2x2 = 0 Combine like terms: x2 + -1x2 = 0 3 + -6x + 0 + -2x2 = 0 3 + -6x + -2x2 = 0 Solving 3 + -6x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.5 + 3x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 3x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 3x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 3x + x2 = 0 + 1.5 3x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 3x + x2 = 1.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 1.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1.5 + 2.25 Combine like terms: 1.5 + 2.25 = 3.75 2.25 + 3x + x2 = 3.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + 1.5) equal to 1.936491673 and -1.936491673.Subproblem 1
x + 1.5 = 1.936491673 Simplifying x + 1.5 = 1.936491673 Reorder the terms: 1.5 + x = 1.936491673 Solving 1.5 + x = 1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.936491673 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.936491673 + -1.5 x = 1.936491673 + -1.5 Combine like terms: 1.936491673 + -1.5 = 0.436491673 x = 0.436491673 Simplifying x = 0.436491673Subproblem 2
x + 1.5 = -1.936491673 Simplifying x + 1.5 = -1.936491673 Reorder the terms: 1.5 + x = -1.936491673 Solving 1.5 + x = -1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.936491673 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.936491673 + -1.5 x = -1.936491673 + -1.5 Combine like terms: -1.936491673 + -1.5 = -3.436491673 x = -3.436491673 Simplifying x = -3.436491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.436491673, -3.436491673}
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