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Simplifying (x + 1)(x + -1) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 Reorder the terms: (1 + x)(x + -1) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 Reorder the terms: (1 + x)(-1 + x) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 Multiply (1 + x) * (-1 + x) (1(-1 + x) + x(-1 + x)) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 ((-1 * 1 + x * 1) + x(-1 + x)) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 ((-1 + 1x) + x(-1 + x)) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 (-1 + 1x + (-1 * x + x * x)) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 (-1 + 1x + (-1x + x2)) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 Combine like terms: 1x + -1x = 0 (-1 + 0 + x2) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 (-1 + x2) + -2x + (2x + 1)(2x + 1) = 4(x + 2)(x + 2) + 8 Reorder the terms: -1 + x2 + -2x + (1 + 2x)(2x + 1) = 4(x + 2)(x + 2) + 8 Reorder the terms: -1 + x2 + -2x + (1 + 2x)(1 + 2x) = 4(x + 2)(x + 2) + 8 Multiply (1 + 2x) * (1 + 2x) -1 + x2 + -2x + (1(1 + 2x) + 2x * (1 + 2x)) = 4(x + 2)(x + 2) + 8 -1 + x2 + -2x + ((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 4(x + 2)(x + 2) + 8 -1 + x2 + -2x + ((1 + 2x) + 2x * (1 + 2x)) = 4(x + 2)(x + 2) + 8 -1 + x2 + -2x + (1 + 2x + (1 * 2x + 2x * 2x)) = 4(x + 2)(x + 2) + 8 -1 + x2 + -2x + (1 + 2x + (2x + 4x2)) = 4(x + 2)(x + 2) + 8 Combine like terms: 2x + 2x = 4x -1 + x2 + -2x + (1 + 4x + 4x2) = 4(x + 2)(x + 2) + 8 Reorder the terms: -1 + 1 + -2x + 4x + x2 + 4x2 = 4(x + 2)(x + 2) + 8 Combine like terms: -1 + 1 = 0 0 + -2x + 4x + x2 + 4x2 = 4(x + 2)(x + 2) + 8 -2x + 4x + x2 + 4x2 = 4(x + 2)(x + 2) + 8 Combine like terms: -2x + 4x = 2x 2x + x2 + 4x2 = 4(x + 2)(x + 2) + 8 Combine like terms: x2 + 4x2 = 5x2 2x + 5x2 = 4(x + 2)(x + 2) + 8 Reorder the terms: 2x + 5x2 = 4(2 + x)(x + 2) + 8 Reorder the terms: 2x + 5x2 = 4(2 + x)(2 + x) + 8 Multiply (2 + x) * (2 + x) 2x + 5x2 = 4(2(2 + x) + x(2 + x)) + 8 2x + 5x2 = 4((2 * 2 + x * 2) + x(2 + x)) + 8 2x + 5x2 = 4((4 + 2x) + x(2 + x)) + 8 2x + 5x2 = 4(4 + 2x + (2 * x + x * x)) + 8 2x + 5x2 = 4(4 + 2x + (2x + x2)) + 8 Combine like terms: 2x + 2x = 4x 2x + 5x2 = 4(4 + 4x + x2) + 8 2x + 5x2 = (4 * 4 + 4x * 4 + x2 * 4) + 8 2x + 5x2 = (16 + 16x + 4x2) + 8 Reorder the terms: 2x + 5x2 = 16 + 8 + 16x + 4x2 Combine like terms: 16 + 8 = 24 2x + 5x2 = 24 + 16x + 4x2 Solving 2x + 5x2 = 24 + 16x + 4x2 Solving for variable 'x'. Reorder the terms: -24 + 2x + -16x + 5x2 + -4x2 = 24 + 16x + 4x2 + -24 + -16x + -4x2 Combine like terms: 2x + -16x = -14x -24 + -14x + 5x2 + -4x2 = 24 + 16x + 4x2 + -24 + -16x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 -24 + -14x + 1x2 = 24 + 16x + 4x2 + -24 + -16x + -4x2 Reorder the terms: -24 + -14x + 1x2 = 24 + -24 + 16x + -16x + 4x2 + -4x2 Combine like terms: 24 + -24 = 0 -24 + -14x + 1x2 = 0 + 16x + -16x + 4x2 + -4x2 -24 + -14x + 1x2 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 -24 + -14x + 1x2 = 0 + 4x2 + -4x2 -24 + -14x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -24 + -14x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -14x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -14x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -14x + x2 = 0 + 24 -14x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -14x + x2 = 24 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 24 + 49 Reorder the terms: 49 + -14x + x2 = 24 + 49 Combine like terms: 24 + 49 = 73 49 + -14x + x2 = 73 Factor a perfect square on the left side: (x + -7)(x + -7) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -7) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -7 = 8.544003745 Simplifying x + -7 = 8.544003745 Reorder the terms: -7 + x = 8.544003745 Solving -7 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.544003745 + 7 x = 8.544003745 + 7 Combine like terms: 8.544003745 + 7 = 15.544003745 x = 15.544003745 Simplifying x = 15.544003745Subproblem 2
x + -7 = -8.544003745 Simplifying x + -7 = -8.544003745 Reorder the terms: -7 + x = -8.544003745 Solving -7 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -8.544003745 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.544003745 + 7 x = -8.544003745 + 7 Combine like terms: -8.544003745 + 7 = -1.544003745 x = -1.544003745 Simplifying x = -1.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.544003745, -1.544003745}
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