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Simplifying 5(x + 2)(x + 2) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 Reorder the terms: 5(2 + x)(x + 2) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 Reorder the terms: 5(2 + x)(2 + x) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 Multiply (2 + x) * (2 + x) 5(2(2 + x) + x(2 + x)) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 5((2 * 2 + x * 2) + x(2 + x)) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 5((4 + 2x) + x(2 + x)) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 5(4 + 2x + (2 * x + x * x)) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 5(4 + 2x + (2x + x2)) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 Combine like terms: 2x + 2x = 4x 5(4 + 4x + x2) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 (4 * 5 + 4x * 5 + x2 * 5) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 (20 + 20x + 5x2) + -1(x + -5)(x + -5) = (2x + -3)(2x + -3) + 19 Reorder the terms: 20 + 20x + 5x2 + -1(-5 + x)(x + -5) = (2x + -3)(2x + -3) + 19 Reorder the terms: 20 + 20x + 5x2 + -1(-5 + x)(-5 + x) = (2x + -3)(2x + -3) + 19 Multiply (-5 + x) * (-5 + x) 20 + 20x + 5x2 + -1(-5(-5 + x) + x(-5 + x)) = (2x + -3)(2x + -3) + 19 20 + 20x + 5x2 + -1((-5 * -5 + x * -5) + x(-5 + x)) = (2x + -3)(2x + -3) + 19 20 + 20x + 5x2 + -1((25 + -5x) + x(-5 + x)) = (2x + -3)(2x + -3) + 19 20 + 20x + 5x2 + -1(25 + -5x + (-5 * x + x * x)) = (2x + -3)(2x + -3) + 19 20 + 20x + 5x2 + -1(25 + -5x + (-5x + x2)) = (2x + -3)(2x + -3) + 19 Combine like terms: -5x + -5x = -10x 20 + 20x + 5x2 + -1(25 + -10x + x2) = (2x + -3)(2x + -3) + 19 20 + 20x + 5x2 + (25 * -1 + -10x * -1 + x2 * -1) = (2x + -3)(2x + -3) + 19 20 + 20x + 5x2 + (-25 + 10x + -1x2) = (2x + -3)(2x + -3) + 19 Reorder the terms: 20 + -25 + 20x + 10x + 5x2 + -1x2 = (2x + -3)(2x + -3) + 19 Combine like terms: 20 + -25 = -5 -5 + 20x + 10x + 5x2 + -1x2 = (2x + -3)(2x + -3) + 19 Combine like terms: 20x + 10x = 30x -5 + 30x + 5x2 + -1x2 = (2x + -3)(2x + -3) + 19 Combine like terms: 5x2 + -1x2 = 4x2 -5 + 30x + 4x2 = (2x + -3)(2x + -3) + 19 Reorder the terms: -5 + 30x + 4x2 = (-3 + 2x)(2x + -3) + 19 Reorder the terms: -5 + 30x + 4x2 = (-3 + 2x)(-3 + 2x) + 19 Multiply (-3 + 2x) * (-3 + 2x) -5 + 30x + 4x2 = (-3(-3 + 2x) + 2x * (-3 + 2x)) + 19 -5 + 30x + 4x2 = ((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) + 19 -5 + 30x + 4x2 = ((9 + -6x) + 2x * (-3 + 2x)) + 19 -5 + 30x + 4x2 = (9 + -6x + (-3 * 2x + 2x * 2x)) + 19 -5 + 30x + 4x2 = (9 + -6x + (-6x + 4x2)) + 19 Combine like terms: -6x + -6x = -12x -5 + 30x + 4x2 = (9 + -12x + 4x2) + 19 Reorder the terms: -5 + 30x + 4x2 = 9 + 19 + -12x + 4x2 Combine like terms: 9 + 19 = 28 -5 + 30x + 4x2 = 28 + -12x + 4x2 Add '-4x2' to each side of the equation. -5 + 30x + 4x2 + -4x2 = 28 + -12x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + 30x + 0 = 28 + -12x + 4x2 + -4x2 -5 + 30x = 28 + -12x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + 30x = 28 + -12x + 0 -5 + 30x = 28 + -12x Solving -5 + 30x = 28 + -12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12x' to each side of the equation. -5 + 30x + 12x = 28 + -12x + 12x Combine like terms: 30x + 12x = 42x -5 + 42x = 28 + -12x + 12x Combine like terms: -12x + 12x = 0 -5 + 42x = 28 + 0 -5 + 42x = 28 Add '5' to each side of the equation. -5 + 5 + 42x = 28 + 5 Combine like terms: -5 + 5 = 0 0 + 42x = 28 + 5 42x = 28 + 5 Combine like terms: 28 + 5 = 33 42x = 33 Divide each side by '42'. x = 0.7857142857 Simplifying x = 0.7857142857
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