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Simplifying 3(6x + -2)(6x + -1) + -1(2x + -3)(5x + 6) = 0 Reorder the terms: 3(-2 + 6x)(6x + -1) + -1(2x + -3)(5x + 6) = 0 Reorder the terms: 3(-2 + 6x)(-1 + 6x) + -1(2x + -3)(5x + 6) = 0 Multiply (-2 + 6x) * (-1 + 6x) 3(-2(-1 + 6x) + 6x * (-1 + 6x)) + -1(2x + -3)(5x + 6) = 0 3((-1 * -2 + 6x * -2) + 6x * (-1 + 6x)) + -1(2x + -3)(5x + 6) = 0 3((2 + -12x) + 6x * (-1 + 6x)) + -1(2x + -3)(5x + 6) = 0 3(2 + -12x + (-1 * 6x + 6x * 6x)) + -1(2x + -3)(5x + 6) = 0 3(2 + -12x + (-6x + 36x2)) + -1(2x + -3)(5x + 6) = 0 Combine like terms: -12x + -6x = -18x 3(2 + -18x + 36x2) + -1(2x + -3)(5x + 6) = 0 (2 * 3 + -18x * 3 + 36x2 * 3) + -1(2x + -3)(5x + 6) = 0 (6 + -54x + 108x2) + -1(2x + -3)(5x + 6) = 0 Reorder the terms: 6 + -54x + 108x2 + -1(-3 + 2x)(5x + 6) = 0 Reorder the terms: 6 + -54x + 108x2 + -1(-3 + 2x)(6 + 5x) = 0 Multiply (-3 + 2x) * (6 + 5x) 6 + -54x + 108x2 + -1(-3(6 + 5x) + 2x * (6 + 5x)) = 0 6 + -54x + 108x2 + -1((6 * -3 + 5x * -3) + 2x * (6 + 5x)) = 0 6 + -54x + 108x2 + -1((-18 + -15x) + 2x * (6 + 5x)) = 0 6 + -54x + 108x2 + -1(-18 + -15x + (6 * 2x + 5x * 2x)) = 0 6 + -54x + 108x2 + -1(-18 + -15x + (12x + 10x2)) = 0 Combine like terms: -15x + 12x = -3x 6 + -54x + 108x2 + -1(-18 + -3x + 10x2) = 0 6 + -54x + 108x2 + (-18 * -1 + -3x * -1 + 10x2 * -1) = 0 6 + -54x + 108x2 + (18 + 3x + -10x2) = 0 Reorder the terms: 6 + 18 + -54x + 3x + 108x2 + -10x2 = 0 Combine like terms: 6 + 18 = 24 24 + -54x + 3x + 108x2 + -10x2 = 0 Combine like terms: -54x + 3x = -51x 24 + -51x + 108x2 + -10x2 = 0 Combine like terms: 108x2 + -10x2 = 98x2 24 + -51x + 98x2 = 0 Solving 24 + -51x + 98x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 98 the coefficient of the squared term: Divide each side by '98'. 0.2448979592 + -0.5204081633x + x2 = 0 Move the constant term to the right: Add '-0.2448979592' to each side of the equation. 0.2448979592 + -0.5204081633x + -0.2448979592 + x2 = 0 + -0.2448979592 Reorder the terms: 0.2448979592 + -0.2448979592 + -0.5204081633x + x2 = 0 + -0.2448979592 Combine like terms: 0.2448979592 + -0.2448979592 = 0.0000000000 0.0000000000 + -0.5204081633x + x2 = 0 + -0.2448979592 -0.5204081633x + x2 = 0 + -0.2448979592 Combine like terms: 0 + -0.2448979592 = -0.2448979592 -0.5204081633x + x2 = -0.2448979592 The x term is -0.5204081633x. Take half its coefficient (-0.2602040817). Square it (0.06770616413) and add it to both sides. Add '0.06770616413' to each side of the equation. -0.5204081633x + 0.06770616413 + x2 = -0.2448979592 + 0.06770616413 Reorder the terms: 0.06770616413 + -0.5204081633x + x2 = -0.2448979592 + 0.06770616413 Combine like terms: -0.2448979592 + 0.06770616413 = -0.17719179507 0.06770616413 + -0.5204081633x + x2 = -0.17719179507 Factor a perfect square on the left side: (x + -0.2602040817)(x + -0.2602040817) = -0.17719179507 Can't calculate square root of the right side. The solution to this equation could not be determined.
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