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Simplifying (7x + 1)(1 + -1x) + -1(2x + -2)(x + 3) = 0 Reorder the terms: (1 + 7x)(1 + -1x) + -1(2x + -2)(x + 3) = 0 Multiply (1 + 7x) * (1 + -1x) (1(1 + -1x) + 7x * (1 + -1x)) + -1(2x + -2)(x + 3) = 0 ((1 * 1 + -1x * 1) + 7x * (1 + -1x)) + -1(2x + -2)(x + 3) = 0 ((1 + -1x) + 7x * (1 + -1x)) + -1(2x + -2)(x + 3) = 0 (1 + -1x + (1 * 7x + -1x * 7x)) + -1(2x + -2)(x + 3) = 0 (1 + -1x + (7x + -7x2)) + -1(2x + -2)(x + 3) = 0 Combine like terms: -1x + 7x = 6x (1 + 6x + -7x2) + -1(2x + -2)(x + 3) = 0 Reorder the terms: 1 + 6x + -7x2 + -1(-2 + 2x)(x + 3) = 0 Reorder the terms: 1 + 6x + -7x2 + -1(-2 + 2x)(3 + x) = 0 Multiply (-2 + 2x) * (3 + x) 1 + 6x + -7x2 + -1(-2(3 + x) + 2x * (3 + x)) = 0 1 + 6x + -7x2 + -1((3 * -2 + x * -2) + 2x * (3 + x)) = 0 1 + 6x + -7x2 + -1((-6 + -2x) + 2x * (3 + x)) = 0 1 + 6x + -7x2 + -1(-6 + -2x + (3 * 2x + x * 2x)) = 0 1 + 6x + -7x2 + -1(-6 + -2x + (6x + 2x2)) = 0 Combine like terms: -2x + 6x = 4x 1 + 6x + -7x2 + -1(-6 + 4x + 2x2) = 0 1 + 6x + -7x2 + (-6 * -1 + 4x * -1 + 2x2 * -1) = 0 1 + 6x + -7x2 + (6 + -4x + -2x2) = 0 Reorder the terms: 1 + 6 + 6x + -4x + -7x2 + -2x2 = 0 Combine like terms: 1 + 6 = 7 7 + 6x + -4x + -7x2 + -2x2 = 0 Combine like terms: 6x + -4x = 2x 7 + 2x + -7x2 + -2x2 = 0 Combine like terms: -7x2 + -2x2 = -9x2 7 + 2x + -9x2 = 0 Solving 7 + 2x + -9x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x)(7 + 9x) = 0Subproblem 1
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 = 1Subproblem 2
Set the factor '(7 + 9x)' equal to zero and attempt to solve: Simplifying 7 + 9x = 0 Solving 7 + 9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 9x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9x = 0 + -7 9x = 0 + -7 Combine like terms: 0 + -7 = -7 9x = -7 Divide each side by '9'. x = -0.7777777778 Simplifying x = -0.7777777778Solution
x = {1, -0.7777777778}
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