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Simplifying 3(4x + -6) + -1(5x + 4) = 2x[8x + -1(5 + x)] Reorder the terms: 3(-6 + 4x) + -1(5x + 4) = 2x[8x + -1(5 + x)] (-6 * 3 + 4x * 3) + -1(5x + 4) = 2x[8x + -1(5 + x)] (-18 + 12x) + -1(5x + 4) = 2x[8x + -1(5 + x)] Reorder the terms: -18 + 12x + -1(4 + 5x) = 2x[8x + -1(5 + x)] -18 + 12x + (4 * -1 + 5x * -1) = 2x[8x + -1(5 + x)] -18 + 12x + (-4 + -5x) = 2x[8x + -1(5 + x)] Reorder the terms: -18 + -4 + 12x + -5x = 2x[8x + -1(5 + x)] Combine like terms: -18 + -4 = -22 -22 + 12x + -5x = 2x[8x + -1(5 + x)] Combine like terms: 12x + -5x = 7x -22 + 7x = 2x[8x + -1(5 + x)] -22 + 7x = 2x[8x + (5 * -1 + x * -1)] -22 + 7x = 2x[8x + (-5 + -1x)] Reorder the terms: -22 + 7x = 2x[-5 + 8x + -1x] Combine like terms: 8x + -1x = 7x -22 + 7x = 2x[-5 + 7x] -22 + 7x = [-5 * 2x + 7x * 2x] -22 + 7x = [-10x + 14x2] Solving -22 + 7x = -10x + 14x2 Solving for variable 'x'. Combine like terms: 7x + 10x = 17x -22 + 17x + -14x2 = -10x + 14x2 + 10x + -14x2 Reorder the terms: -22 + 17x + -14x2 = -10x + 10x + 14x2 + -14x2 Combine like terms: -10x + 10x = 0 -22 + 17x + -14x2 = 0 + 14x2 + -14x2 -22 + 17x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -22 + 17x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. 1.571428571 + -1.214285714x + x2 = 0 Move the constant term to the right: Add '-1.571428571' to each side of the equation. 1.571428571 + -1.214285714x + -1.571428571 + x2 = 0 + -1.571428571 Reorder the terms: 1.571428571 + -1.571428571 + -1.214285714x + x2 = 0 + -1.571428571 Combine like terms: 1.571428571 + -1.571428571 = 0.000000000 0.000000000 + -1.214285714x + x2 = 0 + -1.571428571 -1.214285714x + x2 = 0 + -1.571428571 Combine like terms: 0 + -1.571428571 = -1.571428571 -1.214285714x + x2 = -1.571428571 The x term is -1.214285714x. Take half its coefficient (-0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. -1.214285714x + 0.3686224488 + x2 = -1.571428571 + 0.3686224488 Reorder the terms: 0.3686224488 + -1.214285714x + x2 = -1.571428571 + 0.3686224488 Combine like terms: -1.571428571 + 0.3686224488 = -1.2028061222 0.3686224488 + -1.214285714x + x2 = -1.2028061222 Factor a perfect square on the left side: (x + -0.607142857)(x + -0.607142857) = -1.2028061222 Can't calculate square root of the right side. The solution to this equation could not be determined.
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