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Simplifying 16(x + -5)(x + 20) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Reorder the terms: 16(-5 + x)(x + 20) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Reorder the terms: 16(-5 + x)(20 + x) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Multiply (-5 + x) * (20 + x) 16(-5(20 + x) + x(20 + x)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) 16((20 * -5 + x * -5) + x(20 + x)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) 16((-100 + -5x) + x(20 + x)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) 16(-100 + -5x + (20 * x + x * x)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) 16(-100 + -5x + (20x + x2)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Combine like terms: -5x + 20x = 15x 16(-100 + 15x + x2) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) (-100 * 16 + 15x * 16 + x2 * 16) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) (-1600 + 240x + 16x2) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Reorder the terms: -1600 + 240x + 16x2 + 4(12 + x)(x + -4) = 64(x + -3)(x + 6) Reorder the terms: -1600 + 240x + 16x2 + 4(12 + x)(-4 + x) = 64(x + -3)(x + 6) Multiply (12 + x) * (-4 + x) -1600 + 240x + 16x2 + 4(12(-4 + x) + x(-4 + x)) = 64(x + -3)(x + 6) -1600 + 240x + 16x2 + 4((-4 * 12 + x * 12) + x(-4 + x)) = 64(x + -3)(x + 6) -1600 + 240x + 16x2 + 4((-48 + 12x) + x(-4 + x)) = 64(x + -3)(x + 6) -1600 + 240x + 16x2 + 4(-48 + 12x + (-4 * x + x * x)) = 64(x + -3)(x + 6) -1600 + 240x + 16x2 + 4(-48 + 12x + (-4x + x2)) = 64(x + -3)(x + 6) Combine like terms: 12x + -4x = 8x -1600 + 240x + 16x2 + 4(-48 + 8x + x2) = 64(x + -3)(x + 6) -1600 + 240x + 16x2 + (-48 * 4 + 8x * 4 + x2 * 4) = 64(x + -3)(x + 6) -1600 + 240x + 16x2 + (-192 + 32x + 4x2) = 64(x + -3)(x + 6) Reorder the terms: -1600 + -192 + 240x + 32x + 16x2 + 4x2 = 64(x + -3)(x + 6) Combine like terms: -1600 + -192 = -1792 -1792 + 240x + 32x + 16x2 + 4x2 = 64(x + -3)(x + 6) Combine like terms: 240x + 32x = 272x -1792 + 272x + 16x2 + 4x2 = 64(x + -3)(x + 6) Combine like terms: 16x2 + 4x2 = 20x2 -1792 + 272x + 20x2 = 64(x + -3)(x + 6) Reorder the terms: -1792 + 272x + 20x2 = 64(-3 + x)(x + 6) Reorder the terms: -1792 + 272x + 20x2 = 64(-3 + x)(6 + x) Multiply (-3 + x) * (6 + x) -1792 + 272x + 20x2 = 64(-3(6 + x) + x(6 + x)) -1792 + 272x + 20x2 = 64((6 * -3 + x * -3) + x(6 + x)) -1792 + 272x + 20x2 = 64((-18 + -3x) + x(6 + x)) -1792 + 272x + 20x2 = 64(-18 + -3x + (6 * x + x * x)) -1792 + 272x + 20x2 = 64(-18 + -3x + (6x + x2)) Combine like terms: -3x + 6x = 3x -1792 + 272x + 20x2 = 64(-18 + 3x + x2) -1792 + 272x + 20x2 = (-18 * 64 + 3x * 64 + x2 * 64) -1792 + 272x + 20x2 = (-1152 + 192x + 64x2) Solving -1792 + 272x + 20x2 = -1152 + 192x + 64x2 Solving for variable 'x'. Reorder the terms: -1792 + 1152 + 272x + -192x + 20x2 + -64x2 = -1152 + 192x + 64x2 + 1152 + -192x + -64x2 Combine like terms: -1792 + 1152 = -640 -640 + 272x + -192x + 20x2 + -64x2 = -1152 + 192x + 64x2 + 1152 + -192x + -64x2 Combine like terms: 272x + -192x = 80x -640 + 80x + 20x2 + -64x2 = -1152 + 192x + 64x2 + 1152 + -192x + -64x2 Combine like terms: 20x2 + -64x2 = -44x2 -640 + 80x + -44x2 = -1152 + 192x + 64x2 + 1152 + -192x + -64x2 Reorder the terms: -640 + 80x + -44x2 = -1152 + 1152 + 192x + -192x + 64x2 + -64x2 Combine like terms: -1152 + 1152 = 0 -640 + 80x + -44x2 = 0 + 192x + -192x + 64x2 + -64x2 -640 + 80x + -44x2 = 192x + -192x + 64x2 + -64x2 Combine like terms: 192x + -192x = 0 -640 + 80x + -44x2 = 0 + 64x2 + -64x2 -640 + 80x + -44x2 = 64x2 + -64x2 Combine like terms: 64x2 + -64x2 = 0 -640 + 80x + -44x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-160 + 20x + -11x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-160 + 20x + -11x2)' equal to zero and attempt to solve: Simplifying -160 + 20x + -11x2 = 0 Solving -160 + 20x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. 14.54545455 + -1.818181818x + x2 = 0 Move the constant term to the right: Add '-14.54545455' to each side of the equation. 14.54545455 + -1.818181818x + -14.54545455 + x2 = 0 + -14.54545455 Reorder the terms: 14.54545455 + -14.54545455 + -1.818181818x + x2 = 0 + -14.54545455 Combine like terms: 14.54545455 + -14.54545455 = 0.00000000 0.00000000 + -1.818181818x + x2 = 0 + -14.54545455 -1.818181818x + x2 = 0 + -14.54545455 Combine like terms: 0 + -14.54545455 = -14.54545455 -1.818181818x + x2 = -14.54545455 The x term is -1.818181818x. Take half its coefficient (-0.909090909). Square it (0.8264462808) and add it to both sides. Add '0.8264462808' to each side of the equation. -1.818181818x + 0.8264462808 + x2 = -14.54545455 + 0.8264462808 Reorder the terms: 0.8264462808 + -1.818181818x + x2 = -14.54545455 + 0.8264462808 Combine like terms: -14.54545455 + 0.8264462808 = -13.7190082692 0.8264462808 + -1.818181818x + x2 = -13.7190082692 Factor a perfect square on the left side: (x + -0.909090909)(x + -0.909090909) = -13.7190082692 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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