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Simplifying (3x + 1)(3x + -1) = (x + 9)(x + 4) + -42 Reorder the terms: (1 + 3x)(3x + -1) = (x + 9)(x + 4) + -42 Reorder the terms: (1 + 3x)(-1 + 3x) = (x + 9)(x + 4) + -42 Multiply (1 + 3x) * (-1 + 3x) (1(-1 + 3x) + 3x * (-1 + 3x)) = (x + 9)(x + 4) + -42 ((-1 * 1 + 3x * 1) + 3x * (-1 + 3x)) = (x + 9)(x + 4) + -42 ((-1 + 3x) + 3x * (-1 + 3x)) = (x + 9)(x + 4) + -42 (-1 + 3x + (-1 * 3x + 3x * 3x)) = (x + 9)(x + 4) + -42 (-1 + 3x + (-3x + 9x2)) = (x + 9)(x + 4) + -42 Combine like terms: 3x + -3x = 0 (-1 + 0 + 9x2) = (x + 9)(x + 4) + -42 (-1 + 9x2) = (x + 9)(x + 4) + -42 Reorder the terms: -1 + 9x2 = (9 + x)(x + 4) + -42 Reorder the terms: -1 + 9x2 = (9 + x)(4 + x) + -42 Multiply (9 + x) * (4 + x) -1 + 9x2 = (9(4 + x) + x(4 + x)) + -42 -1 + 9x2 = ((4 * 9 + x * 9) + x(4 + x)) + -42 -1 + 9x2 = ((36 + 9x) + x(4 + x)) + -42 -1 + 9x2 = (36 + 9x + (4 * x + x * x)) + -42 -1 + 9x2 = (36 + 9x + (4x + x2)) + -42 Combine like terms: 9x + 4x = 13x -1 + 9x2 = (36 + 13x + x2) + -42 Reorder the terms: -1 + 9x2 = 36 + -42 + 13x + x2 Combine like terms: 36 + -42 = -6 -1 + 9x2 = -6 + 13x + x2 Solving -1 + 9x2 = -6 + 13x + x2 Solving for variable 'x'. Reorder the terms: -1 + 6 + -13x + 9x2 + -1x2 = -6 + 13x + x2 + 6 + -13x + -1x2 Combine like terms: -1 + 6 = 5 5 + -13x + 9x2 + -1x2 = -6 + 13x + x2 + 6 + -13x + -1x2 Combine like terms: 9x2 + -1x2 = 8x2 5 + -13x + 8x2 = -6 + 13x + x2 + 6 + -13x + -1x2 Reorder the terms: 5 + -13x + 8x2 = -6 + 6 + 13x + -13x + x2 + -1x2 Combine like terms: -6 + 6 = 0 5 + -13x + 8x2 = 0 + 13x + -13x + x2 + -1x2 5 + -13x + 8x2 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 5 + -13x + 8x2 = 0 + x2 + -1x2 5 + -13x + 8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + -13x + 8x2 = 0 Factor a trinomial. (5 + -8x)(1 + -1x) = 0Subproblem 1
Set the factor '(5 + -8x)' equal to zero and attempt to solve: Simplifying 5 + -8x = 0 Solving 5 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -8x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8x = 0 + -5 -8x = 0 + -5 Combine like terms: 0 + -5 = -5 -8x = -5 Divide each side by '-8'. x = 0.625 Simplifying x = 0.625Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0.625, 1}
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