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Simplifying -13x + -1(x + -4) * 2 + 8(2x + -3) = 8 + -1(x + 5)(x + -5) + -10(x + 1) Reorder the terms: -13x + -1(-4 + x) * 2 + 8(2x + -3) = 8 + -1(x + 5)(x + -5) + -10(x + 1) Reorder the terms for easier multiplication: -13x + -1 * 2(-4 + x) + 8(2x + -3) = 8 + -1(x + 5)(x + -5) + -10(x + 1) Multiply -1 * 2 -13x + -2(-4 + x) + 8(2x + -3) = 8 + -1(x + 5)(x + -5) + -10(x + 1) -13x + (-4 * -2 + x * -2) + 8(2x + -3) = 8 + -1(x + 5)(x + -5) + -10(x + 1) -13x + (8 + -2x) + 8(2x + -3) = 8 + -1(x + 5)(x + -5) + -10(x + 1) Reorder the terms: -13x + 8 + -2x + 8(-3 + 2x) = 8 + -1(x + 5)(x + -5) + -10(x + 1) -13x + 8 + -2x + (-3 * 8 + 2x * 8) = 8 + -1(x + 5)(x + -5) + -10(x + 1) -13x + 8 + -2x + (-24 + 16x) = 8 + -1(x + 5)(x + -5) + -10(x + 1) Reorder the terms: 8 + -24 + -13x + -2x + 16x = 8 + -1(x + 5)(x + -5) + -10(x + 1) Combine like terms: 8 + -24 = -16 -16 + -13x + -2x + 16x = 8 + -1(x + 5)(x + -5) + -10(x + 1) Combine like terms: -13x + -2x = -15x -16 + -15x + 16x = 8 + -1(x + 5)(x + -5) + -10(x + 1) Combine like terms: -15x + 16x = 1x -16 + 1x = 8 + -1(x + 5)(x + -5) + -10(x + 1) Reorder the terms: -16 + 1x = 8 + -1(5 + x)(x + -5) + -10(x + 1) Reorder the terms: -16 + 1x = 8 + -1(5 + x)(-5 + x) + -10(x + 1) Multiply (5 + x) * (-5 + x) -16 + 1x = 8 + -1(5(-5 + x) + x(-5 + x)) + -10(x + 1) -16 + 1x = 8 + -1((-5 * 5 + x * 5) + x(-5 + x)) + -10(x + 1) -16 + 1x = 8 + -1((-25 + 5x) + x(-5 + x)) + -10(x + 1) -16 + 1x = 8 + -1(-25 + 5x + (-5 * x + x * x)) + -10(x + 1) -16 + 1x = 8 + -1(-25 + 5x + (-5x + x2)) + -10(x + 1) Combine like terms: 5x + -5x = 0 -16 + 1x = 8 + -1(-25 + 0 + x2) + -10(x + 1) -16 + 1x = 8 + -1(-25 + x2) + -10(x + 1) -16 + 1x = 8 + (-25 * -1 + x2 * -1) + -10(x + 1) -16 + 1x = 8 + (25 + -1x2) + -10(x + 1) Reorder the terms: -16 + 1x = 8 + 25 + -1x2 + -10(1 + x) -16 + 1x = 8 + 25 + -1x2 + (1 * -10 + x * -10) -16 + 1x = 8 + 25 + -1x2 + (-10 + -10x) Reorder the terms: -16 + 1x = 8 + 25 + -10 + -10x + -1x2 Combine like terms: 8 + 25 = 33 -16 + 1x = 33 + -10 + -10x + -1x2 Combine like terms: 33 + -10 = 23 -16 + 1x = 23 + -10x + -1x2 Solving -16 + 1x = 23 + -10x + -1x2 Solving for variable 'x'. Reorder the terms: -16 + -23 + 1x + 10x + x2 = 23 + -10x + -1x2 + -23 + 10x + x2 Combine like terms: -16 + -23 = -39 -39 + 1x + 10x + x2 = 23 + -10x + -1x2 + -23 + 10x + x2 Combine like terms: 1x + 10x = 11x -39 + 11x + x2 = 23 + -10x + -1x2 + -23 + 10x + x2 Reorder the terms: -39 + 11x + x2 = 23 + -23 + -10x + 10x + -1x2 + x2 Combine like terms: 23 + -23 = 0 -39 + 11x + x2 = 0 + -10x + 10x + -1x2 + x2 -39 + 11x + x2 = -10x + 10x + -1x2 + x2 Combine like terms: -10x + 10x = 0 -39 + 11x + x2 = 0 + -1x2 + x2 -39 + 11x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -39 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 11x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 11x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 11x + x2 = 0 + 39 11x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 11x + x2 = 39 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 39 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 39 + 30.25 Combine like terms: 39 + 30.25 = 69.25 30.25 + 11x + x2 = 69.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + 5.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + 5.5 = 8.321658489 Simplifying x + 5.5 = 8.321658489 Reorder the terms: 5.5 + x = 8.321658489 Solving 5.5 + x = 8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 8.321658489 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 8.321658489 + -5.5 x = 8.321658489 + -5.5 Combine like terms: 8.321658489 + -5.5 = 2.821658489 x = 2.821658489 Simplifying x = 2.821658489Subproblem 2
x + 5.5 = -8.321658489 Simplifying x + 5.5 = -8.321658489 Reorder the terms: 5.5 + x = -8.321658489 Solving 5.5 + x = -8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -8.321658489 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -8.321658489 + -5.5 x = -8.321658489 + -5.5 Combine like terms: -8.321658489 + -5.5 = -13.821658489 x = -13.821658489 Simplifying x = -13.821658489Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.821658489, -13.821658489}
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