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Simplifying 36(x + -5)(x + 20) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Reorder the terms: 36(-5 + x)(x + 20) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Reorder the terms: 36(-5 + x)(20 + x) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Multiply (-5 + x) * (20 + x) 36(-5(20 + x) + x(20 + x)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) 36((20 * -5 + x * -5) + x(20 + x)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) 36((-100 + -5x) + x(20 + x)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) 36(-100 + -5x + (20 * x + x * x)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) 36(-100 + -5x + (20x + x2)) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Combine like terms: -5x + 20x = 15x 36(-100 + 15x + x2) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) (-100 * 36 + 15x * 36 + x2 * 36) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) (-3600 + 540x + 36x2) + 4(x + 12)(x + -4) = 64(x + -3)(x + 6) Reorder the terms: -3600 + 540x + 36x2 + 4(12 + x)(x + -4) = 64(x + -3)(x + 6) Reorder the terms: -3600 + 540x + 36x2 + 4(12 + x)(-4 + x) = 64(x + -3)(x + 6) Multiply (12 + x) * (-4 + x) -3600 + 540x + 36x2 + 4(12(-4 + x) + x(-4 + x)) = 64(x + -3)(x + 6) -3600 + 540x + 36x2 + 4((-4 * 12 + x * 12) + x(-4 + x)) = 64(x + -3)(x + 6) -3600 + 540x + 36x2 + 4((-48 + 12x) + x(-4 + x)) = 64(x + -3)(x + 6) -3600 + 540x + 36x2 + 4(-48 + 12x + (-4 * x + x * x)) = 64(x + -3)(x + 6) -3600 + 540x + 36x2 + 4(-48 + 12x + (-4x + x2)) = 64(x + -3)(x + 6) Combine like terms: 12x + -4x = 8x -3600 + 540x + 36x2 + 4(-48 + 8x + x2) = 64(x + -3)(x + 6) -3600 + 540x + 36x2 + (-48 * 4 + 8x * 4 + x2 * 4) = 64(x + -3)(x + 6) -3600 + 540x + 36x2 + (-192 + 32x + 4x2) = 64(x + -3)(x + 6) Reorder the terms: -3600 + -192 + 540x + 32x + 36x2 + 4x2 = 64(x + -3)(x + 6) Combine like terms: -3600 + -192 = -3792 -3792 + 540x + 32x + 36x2 + 4x2 = 64(x + -3)(x + 6) Combine like terms: 540x + 32x = 572x -3792 + 572x + 36x2 + 4x2 = 64(x + -3)(x + 6) Combine like terms: 36x2 + 4x2 = 40x2 -3792 + 572x + 40x2 = 64(x + -3)(x + 6) Reorder the terms: -3792 + 572x + 40x2 = 64(-3 + x)(x + 6) Reorder the terms: -3792 + 572x + 40x2 = 64(-3 + x)(6 + x) Multiply (-3 + x) * (6 + x) -3792 + 572x + 40x2 = 64(-3(6 + x) + x(6 + x)) -3792 + 572x + 40x2 = 64((6 * -3 + x * -3) + x(6 + x)) -3792 + 572x + 40x2 = 64((-18 + -3x) + x(6 + x)) -3792 + 572x + 40x2 = 64(-18 + -3x + (6 * x + x * x)) -3792 + 572x + 40x2 = 64(-18 + -3x + (6x + x2)) Combine like terms: -3x + 6x = 3x -3792 + 572x + 40x2 = 64(-18 + 3x + x2) -3792 + 572x + 40x2 = (-18 * 64 + 3x * 64 + x2 * 64) -3792 + 572x + 40x2 = (-1152 + 192x + 64x2) Solving -3792 + 572x + 40x2 = -1152 + 192x + 64x2 Solving for variable 'x'. Reorder the terms: -3792 + 1152 + 572x + -192x + 40x2 + -64x2 = -1152 + 192x + 64x2 + 1152 + -192x + -64x2 Combine like terms: -3792 + 1152 = -2640 -2640 + 572x + -192x + 40x2 + -64x2 = -1152 + 192x + 64x2 + 1152 + -192x + -64x2 Combine like terms: 572x + -192x = 380x -2640 + 380x + 40x2 + -64x2 = -1152 + 192x + 64x2 + 1152 + -192x + -64x2 Combine like terms: 40x2 + -64x2 = -24x2 -2640 + 380x + -24x2 = -1152 + 192x + 64x2 + 1152 + -192x + -64x2 Reorder the terms: -2640 + 380x + -24x2 = -1152 + 1152 + 192x + -192x + 64x2 + -64x2 Combine like terms: -1152 + 1152 = 0 -2640 + 380x + -24x2 = 0 + 192x + -192x + 64x2 + -64x2 -2640 + 380x + -24x2 = 192x + -192x + 64x2 + -64x2 Combine like terms: 192x + -192x = 0 -2640 + 380x + -24x2 = 0 + 64x2 + -64x2 -2640 + 380x + -24x2 = 64x2 + -64x2 Combine like terms: 64x2 + -64x2 = 0 -2640 + 380x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-660 + 95x + -6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-660 + 95x + -6x2)' equal to zero and attempt to solve: Simplifying -660 + 95x + -6x2 = 0 Solving -660 + 95x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 110 + -15.83333333x + x2 = 0 Move the constant term to the right: Add '-110' to each side of the equation. 110 + -15.83333333x + -110 + x2 = 0 + -110 Reorder the terms: 110 + -110 + -15.83333333x + x2 = 0 + -110 Combine like terms: 110 + -110 = 0 0 + -15.83333333x + x2 = 0 + -110 -15.83333333x + x2 = 0 + -110 Combine like terms: 0 + -110 = -110 -15.83333333x + x2 = -110 The x term is -15.83333333x. Take half its coefficient (-7.916666665). Square it (62.67361108) and add it to both sides. Add '62.67361108' to each side of the equation. -15.83333333x + 62.67361108 + x2 = -110 + 62.67361108 Reorder the terms: 62.67361108 + -15.83333333x + x2 = -110 + 62.67361108 Combine like terms: -110 + 62.67361108 = -47.32638892 62.67361108 + -15.83333333x + x2 = -47.32638892 Factor a perfect square on the left side: (x + -7.916666665)(x + -7.916666665) = -47.32638892 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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