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Simplifying (x + -1)(x + -1)(x + 1) = (x + 4)(x + -4)(x + 4) + -8518 Reorder the terms: (-1 + x)(x + -1)(x + 1) = (x + 4)(x + -4)(x + 4) + -8518 Reorder the terms: (-1 + x)(-1 + x)(x + 1) = (x + 4)(x + -4)(x + 4) + -8518 Reorder the terms: (-1 + x)(-1 + x)(1 + x) = (x + 4)(x + -4)(x + 4) + -8518 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x))(1 + x) = (x + 4)(x + -4)(x + 4) + -8518 ((-1 * -1 + x * -1) + x(-1 + x))(1 + x) = (x + 4)(x + -4)(x + 4) + -8518 ((1 + -1x) + x(-1 + x))(1 + x) = (x + 4)(x + -4)(x + 4) + -8518 (1 + -1x + (-1 * x + x * x))(1 + x) = (x + 4)(x + -4)(x + 4) + -8518 (1 + -1x + (-1x + x2))(1 + x) = (x + 4)(x + -4)(x + 4) + -8518 Combine like terms: -1x + -1x = -2x (1 + -2x + x2)(1 + x) = (x + 4)(x + -4)(x + 4) + -8518 Multiply (1 + -2x + x2) * (1 + x) (1(1 + x) + -2x * (1 + x) + x2(1 + x)) = (x + 4)(x + -4)(x + 4) + -8518 ((1 * 1 + x * 1) + -2x * (1 + x) + x2(1 + x)) = (x + 4)(x + -4)(x + 4) + -8518 ((1 + 1x) + -2x * (1 + x) + x2(1 + x)) = (x + 4)(x + -4)(x + 4) + -8518 (1 + 1x + (1 * -2x + x * -2x) + x2(1 + x)) = (x + 4)(x + -4)(x + 4) + -8518 (1 + 1x + (-2x + -2x2) + x2(1 + x)) = (x + 4)(x + -4)(x + 4) + -8518 (1 + 1x + -2x + -2x2 + (1 * x2 + x * x2)) = (x + 4)(x + -4)(x + 4) + -8518 (1 + 1x + -2x + -2x2 + (1x2 + x3)) = (x + 4)(x + -4)(x + 4) + -8518 Combine like terms: 1x + -2x = -1x (1 + -1x + -2x2 + 1x2 + x3) = (x + 4)(x + -4)(x + 4) + -8518 Combine like terms: -2x2 + 1x2 = -1x2 (1 + -1x + -1x2 + x3) = (x + 4)(x + -4)(x + 4) + -8518 Reorder the terms: 1 + -1x + -1x2 + x3 = (4 + x)(x + -4)(x + 4) + -8518 Reorder the terms: 1 + -1x + -1x2 + x3 = (4 + x)(-4 + x)(x + 4) + -8518 Reorder the terms: 1 + -1x + -1x2 + x3 = (4 + x)(-4 + x)(4 + x) + -8518 Multiply (4 + x) * (-4 + x) 1 + -1x + -1x2 + x3 = (4(-4 + x) + x(-4 + x))(4 + x) + -8518 1 + -1x + -1x2 + x3 = ((-4 * 4 + x * 4) + x(-4 + x))(4 + x) + -8518 1 + -1x + -1x2 + x3 = ((-16 + 4x) + x(-4 + x))(4 + x) + -8518 1 + -1x + -1x2 + x3 = (-16 + 4x + (-4 * x + x * x))(4 + x) + -8518 1 + -1x + -1x2 + x3 = (-16 + 4x + (-4x + x2))(4 + x) + -8518 Combine like terms: 4x + -4x = 0 1 + -1x + -1x2 + x3 = (-16 + 0 + x2)(4 + x) + -8518 1 + -1x + -1x2 + x3 = (-16 + x2)(4 + x) + -8518 Multiply (-16 + x2) * (4 + x) 1 + -1x + -1x2 + x3 = (-16(4 + x) + x2(4 + x)) + -8518 1 + -1x + -1x2 + x3 = ((4 * -16 + x * -16) + x2(4 + x)) + -8518 1 + -1x + -1x2 + x3 = ((-64 + -16x) + x2(4 + x)) + -8518 1 + -1x + -1x2 + x3 = (-64 + -16x + (4 * x2 + x * x2)) + -8518 1 + -1x + -1x2 + x3 = (-64 + -16x + (4x2 + x3)) + -8518 1 + -1x + -1x2 + x3 = (-64 + -16x + 4x2 + x3) + -8518 Reorder the terms: 1 + -1x + -1x2 + x3 = -64 + -8518 + -16x + 4x2 + x3 Combine like terms: -64 + -8518 = -8582 1 + -1x + -1x2 + x3 = -8582 + -16x + 4x2 + x3 Add '-1x3' to each side of the equation. 1 + -1x + -1x2 + x3 + -1x3 = -8582 + -16x + 4x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 1 + -1x + -1x2 + 0 = -8582 + -16x + 4x2 + x3 + -1x3 1 + -1x + -1x2 = -8582 + -16x + 4x2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 1 + -1x + -1x2 = -8582 + -16x + 4x2 + 0 1 + -1x + -1x2 = -8582 + -16x + 4x2 Solving 1 + -1x + -1x2 = -8582 + -16x + 4x2 Solving for variable 'x'. Reorder the terms: 1 + 8582 + -1x + 16x + -1x2 + -4x2 = -8582 + -16x + 4x2 + 8582 + 16x + -4x2 Combine like terms: 1 + 8582 = 8583 8583 + -1x + 16x + -1x2 + -4x2 = -8582 + -16x + 4x2 + 8582 + 16x + -4x2 Combine like terms: -1x + 16x = 15x 8583 + 15x + -1x2 + -4x2 = -8582 + -16x + 4x2 + 8582 + 16x + -4x2 Combine like terms: -1x2 + -4x2 = -5x2 8583 + 15x + -5x2 = -8582 + -16x + 4x2 + 8582 + 16x + -4x2 Reorder the terms: 8583 + 15x + -5x2 = -8582 + 8582 + -16x + 16x + 4x2 + -4x2 Combine like terms: -8582 + 8582 = 0 8583 + 15x + -5x2 = 0 + -16x + 16x + 4x2 + -4x2 8583 + 15x + -5x2 = -16x + 16x + 4x2 + -4x2 Combine like terms: -16x + 16x = 0 8583 + 15x + -5x2 = 0 + 4x2 + -4x2 8583 + 15x + -5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 8583 + 15x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1716.6 + -3x + x2 = 0 Move the constant term to the right: Add '1716.6' to each side of the equation. -1716.6 + -3x + 1716.6 + x2 = 0 + 1716.6 Reorder the terms: -1716.6 + 1716.6 + -3x + x2 = 0 + 1716.6 Combine like terms: -1716.6 + 1716.6 = 0.0 0.0 + -3x + x2 = 0 + 1716.6 -3x + x2 = 0 + 1716.6 Combine like terms: 0 + 1716.6 = 1716.6 -3x + x2 = 1716.6 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 = 1716.6 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1716.6 + 2.25 Combine like terms: 1716.6 + 2.25 = 1718.85 2.25 + -3x + x2 = 1718.85 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1718.85 Calculate the square root of the right side: 41.459015907 Break this problem into two subproblems by setting (x + -1.5) equal to 41.459015907 and -41.459015907.Subproblem 1
x + -1.5 = 41.459015907 Simplifying x + -1.5 = 41.459015907 Reorder the terms: -1.5 + x = 41.459015907 Solving -1.5 + x = 41.459015907 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 = 41.459015907 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 41.459015907 + 1.5 x = 41.459015907 + 1.5 Combine like terms: 41.459015907 + 1.5 = 42.959015907 x = 42.959015907 Simplifying x = 42.959015907Subproblem 2
x + -1.5 = -41.459015907 Simplifying x + -1.5 = -41.459015907 Reorder the terms: -1.5 + x = -41.459015907 Solving -1.5 + x = -41.459015907 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 = -41.459015907 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -41.459015907 + 1.5 x = -41.459015907 + 1.5 Combine like terms: -41.459015907 + 1.5 = -39.959015907 x = -39.959015907 Simplifying x = -39.959015907Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.959015907, -39.959015907}
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