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Simplifying (x + -3)(x + -3) + 3(x + 1)(x + -1) + 3(1 + 6x) = 0 Reorder the terms: (-3 + x)(x + -3) + 3(x + 1)(x + -1) + 3(1 + 6x) = 0 Reorder the terms: (-3 + x)(-3 + x) + 3(x + 1)(x + -1) + 3(1 + 6x) = 0 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) + 3(x + 1)(x + -1) + 3(1 + 6x) = 0 ((-3 * -3 + x * -3) + x(-3 + x)) + 3(x + 1)(x + -1) + 3(1 + 6x) = 0 ((9 + -3x) + x(-3 + x)) + 3(x + 1)(x + -1) + 3(1 + 6x) = 0 (9 + -3x + (-3 * x + x * x)) + 3(x + 1)(x + -1) + 3(1 + 6x) = 0 (9 + -3x + (-3x + x2)) + 3(x + 1)(x + -1) + 3(1 + 6x) = 0 Combine like terms: -3x + -3x = -6x (9 + -6x + x2) + 3(x + 1)(x + -1) + 3(1 + 6x) = 0 Reorder the terms: 9 + -6x + x2 + 3(1 + x)(x + -1) + 3(1 + 6x) = 0 Reorder the terms: 9 + -6x + x2 + 3(1 + x)(-1 + x) + 3(1 + 6x) = 0 Multiply (1 + x) * (-1 + x) 9 + -6x + x2 + 3(1(-1 + x) + x(-1 + x)) + 3(1 + 6x) = 0 9 + -6x + x2 + 3((-1 * 1 + x * 1) + x(-1 + x)) + 3(1 + 6x) = 0 9 + -6x + x2 + 3((-1 + 1x) + x(-1 + x)) + 3(1 + 6x) = 0 9 + -6x + x2 + 3(-1 + 1x + (-1 * x + x * x)) + 3(1 + 6x) = 0 9 + -6x + x2 + 3(-1 + 1x + (-1x + x2)) + 3(1 + 6x) = 0 Combine like terms: 1x + -1x = 0 9 + -6x + x2 + 3(-1 + 0 + x2) + 3(1 + 6x) = 0 9 + -6x + x2 + 3(-1 + x2) + 3(1 + 6x) = 0 9 + -6x + x2 + (-1 * 3 + x2 * 3) + 3(1 + 6x) = 0 9 + -6x + x2 + (-3 + 3x2) + 3(1 + 6x) = 0 9 + -6x + x2 + -3 + 3x2 + (1 * 3 + 6x * 3) = 0 9 + -6x + x2 + -3 + 3x2 + (3 + 18x) = 0 Reorder the terms: 9 + -3 + 3 + -6x + 18x + x2 + 3x2 = 0 Combine like terms: 9 + -3 = 6 6 + 3 + -6x + 18x + x2 + 3x2 = 0 Combine like terms: 6 + 3 = 9 9 + -6x + 18x + x2 + 3x2 = 0 Combine like terms: -6x + 18x = 12x 9 + 12x + x2 + 3x2 = 0 Combine like terms: x2 + 3x2 = 4x2 9 + 12x + 4x2 = 0 Solving 9 + 12x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + 2x)(3 + 2x) = 0Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {-1.5, -1.5}
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