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Simplifying (x + 9)(x + 7) + -1(-1x + 1)(x + -5) = 0 Reorder the terms: (9 + x)(x + 7) + -1(-1x + 1)(x + -5) = 0 Reorder the terms: (9 + x)(7 + x) + -1(-1x + 1)(x + -5) = 0 Multiply (9 + x) * (7 + x) (9(7 + x) + x(7 + x)) + -1(-1x + 1)(x + -5) = 0 ((7 * 9 + x * 9) + x(7 + x)) + -1(-1x + 1)(x + -5) = 0 ((63 + 9x) + x(7 + x)) + -1(-1x + 1)(x + -5) = 0 (63 + 9x + (7 * x + x * x)) + -1(-1x + 1)(x + -5) = 0 (63 + 9x + (7x + x2)) + -1(-1x + 1)(x + -5) = 0 Combine like terms: 9x + 7x = 16x (63 + 16x + x2) + -1(-1x + 1)(x + -5) = 0 Reorder the terms: 63 + 16x + x2 + -1(1 + -1x)(x + -5) = 0 Reorder the terms: 63 + 16x + x2 + -1(1 + -1x)(-5 + x) = 0 Multiply (1 + -1x) * (-5 + x) 63 + 16x + x2 + -1(1(-5 + x) + -1x * (-5 + x)) = 0 63 + 16x + x2 + -1((-5 * 1 + x * 1) + -1x * (-5 + x)) = 0 63 + 16x + x2 + -1((-5 + 1x) + -1x * (-5 + x)) = 0 63 + 16x + x2 + -1(-5 + 1x + (-5 * -1x + x * -1x)) = 0 63 + 16x + x2 + -1(-5 + 1x + (5x + -1x2)) = 0 Combine like terms: 1x + 5x = 6x 63 + 16x + x2 + -1(-5 + 6x + -1x2) = 0 63 + 16x + x2 + (-5 * -1 + 6x * -1 + -1x2 * -1) = 0 63 + 16x + x2 + (5 + -6x + 1x2) = 0 Reorder the terms: 63 + 5 + 16x + -6x + x2 + 1x2 = 0 Combine like terms: 63 + 5 = 68 68 + 16x + -6x + x2 + 1x2 = 0 Combine like terms: 16x + -6x = 10x 68 + 10x + x2 + 1x2 = 0 Combine like terms: x2 + 1x2 = 2x2 68 + 10x + 2x2 = 0 Solving 68 + 10x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(34 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(34 + 5x + x2)' equal to zero and attempt to solve: Simplifying 34 + 5x + x2 = 0 Solving 34 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + 5x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + 5x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 5x + x2 = 0 + -34 5x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 5x + x2 = -34 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -34 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -34 + 6.25 Combine like terms: -34 + 6.25 = -27.75 6.25 + 5x + x2 = -27.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -27.75 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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