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Simplifying (2x + -3)(2x + -3) + -1(x + -1)(x + -1) = 0 Reorder the terms: (-3 + 2x)(2x + -3) + -1(x + -1)(x + -1) = 0 Reorder the terms: (-3 + 2x)(-3 + 2x) + -1(x + -1)(x + -1) = 0 Multiply (-3 + 2x) * (-3 + 2x) (-3(-3 + 2x) + 2x * (-3 + 2x)) + -1(x + -1)(x + -1) = 0 ((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) + -1(x + -1)(x + -1) = 0 ((9 + -6x) + 2x * (-3 + 2x)) + -1(x + -1)(x + -1) = 0 (9 + -6x + (-3 * 2x + 2x * 2x)) + -1(x + -1)(x + -1) = 0 (9 + -6x + (-6x + 4x2)) + -1(x + -1)(x + -1) = 0 Combine like terms: -6x + -6x = -12x (9 + -12x + 4x2) + -1(x + -1)(x + -1) = 0 Reorder the terms: 9 + -12x + 4x2 + -1(-1 + x)(x + -1) = 0 Reorder the terms: 9 + -12x + 4x2 + -1(-1 + x)(-1 + x) = 0 Multiply (-1 + x) * (-1 + x) 9 + -12x + 4x2 + -1(-1(-1 + x) + x(-1 + x)) = 0 9 + -12x + 4x2 + -1((-1 * -1 + x * -1) + x(-1 + x)) = 0 9 + -12x + 4x2 + -1((1 + -1x) + x(-1 + x)) = 0 9 + -12x + 4x2 + -1(1 + -1x + (-1 * x + x * x)) = 0 9 + -12x + 4x2 + -1(1 + -1x + (-1x + x2)) = 0 Combine like terms: -1x + -1x = -2x 9 + -12x + 4x2 + -1(1 + -2x + x2) = 0 9 + -12x + 4x2 + (1 * -1 + -2x * -1 + x2 * -1) = 0 9 + -12x + 4x2 + (-1 + 2x + -1x2) = 0 Reorder the terms: 9 + -1 + -12x + 2x + 4x2 + -1x2 = 0 Combine like terms: 9 + -1 = 8 8 + -12x + 2x + 4x2 + -1x2 = 0 Combine like terms: -12x + 2x = -10x 8 + -10x + 4x2 + -1x2 = 0 Combine like terms: 4x2 + -1x2 = 3x2 8 + -10x + 3x2 = 0 Solving 8 + -10x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (4 + -3x)(2 + -1x) = 0Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {1.333333333, 2}
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