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Simplifying (x + 5)(x + 4) + -1(-8x + -5)(x + 2) = 0 Reorder the terms: (5 + x)(x + 4) + -1(-8x + -5)(x + 2) = 0 Reorder the terms: (5 + x)(4 + x) + -1(-8x + -5)(x + 2) = 0 Multiply (5 + x) * (4 + x) (5(4 + x) + x(4 + x)) + -1(-8x + -5)(x + 2) = 0 ((4 * 5 + x * 5) + x(4 + x)) + -1(-8x + -5)(x + 2) = 0 ((20 + 5x) + x(4 + x)) + -1(-8x + -5)(x + 2) = 0 (20 + 5x + (4 * x + x * x)) + -1(-8x + -5)(x + 2) = 0 (20 + 5x + (4x + x2)) + -1(-8x + -5)(x + 2) = 0 Combine like terms: 5x + 4x = 9x (20 + 9x + x2) + -1(-8x + -5)(x + 2) = 0 Reorder the terms: 20 + 9x + x2 + -1(-5 + -8x)(x + 2) = 0 Reorder the terms: 20 + 9x + x2 + -1(-5 + -8x)(2 + x) = 0 Multiply (-5 + -8x) * (2 + x) 20 + 9x + x2 + -1(-5(2 + x) + -8x * (2 + x)) = 0 20 + 9x + x2 + -1((2 * -5 + x * -5) + -8x * (2 + x)) = 0 20 + 9x + x2 + -1((-10 + -5x) + -8x * (2 + x)) = 0 20 + 9x + x2 + -1(-10 + -5x + (2 * -8x + x * -8x)) = 0 20 + 9x + x2 + -1(-10 + -5x + (-16x + -8x2)) = 0 Combine like terms: -5x + -16x = -21x 20 + 9x + x2 + -1(-10 + -21x + -8x2) = 0 20 + 9x + x2 + (-10 * -1 + -21x * -1 + -8x2 * -1) = 0 20 + 9x + x2 + (10 + 21x + 8x2) = 0 Reorder the terms: 20 + 10 + 9x + 21x + x2 + 8x2 = 0 Combine like terms: 20 + 10 = 30 30 + 9x + 21x + x2 + 8x2 = 0 Combine like terms: 9x + 21x = 30x 30 + 30x + x2 + 8x2 = 0 Combine like terms: x2 + 8x2 = 9x2 30 + 30x + 9x2 = 0 Solving 30 + 30x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 10x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + 10x + 3x2)' equal to zero and attempt to solve: Simplifying 10 + 10x + 3x2 = 0 Solving 10 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 3.333333333x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 3.333333333x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + -3.333333333 3.333333333x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 3.333333333x + x2 = -3.333333333 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = -3.333333333 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -3.333333333 + 2.777777779 Combine like terms: -3.333333333 + 2.777777779 = -0.555555554 2.777777779 + 3.333333333x + x2 = -0.555555554 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = -0.555555554 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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