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Simplifying (x + -3)(2x + -4) + -1(x + 1)(x + -5) = 0 Reorder the terms: (-3 + x)(2x + -4) + -1(x + 1)(x + -5) = 0 Reorder the terms: (-3 + x)(-4 + 2x) + -1(x + 1)(x + -5) = 0 Multiply (-3 + x) * (-4 + 2x) (-3(-4 + 2x) + x(-4 + 2x)) + -1(x + 1)(x + -5) = 0 ((-4 * -3 + 2x * -3) + x(-4 + 2x)) + -1(x + 1)(x + -5) = 0 ((12 + -6x) + x(-4 + 2x)) + -1(x + 1)(x + -5) = 0 (12 + -6x + (-4 * x + 2x * x)) + -1(x + 1)(x + -5) = 0 (12 + -6x + (-4x + 2x2)) + -1(x + 1)(x + -5) = 0 Combine like terms: -6x + -4x = -10x (12 + -10x + 2x2) + -1(x + 1)(x + -5) = 0 Reorder the terms: 12 + -10x + 2x2 + -1(1 + x)(x + -5) = 0 Reorder the terms: 12 + -10x + 2x2 + -1(1 + x)(-5 + x) = 0 Multiply (1 + x) * (-5 + x) 12 + -10x + 2x2 + -1(1(-5 + x) + x(-5 + x)) = 0 12 + -10x + 2x2 + -1((-5 * 1 + x * 1) + x(-5 + x)) = 0 12 + -10x + 2x2 + -1((-5 + 1x) + x(-5 + x)) = 0 12 + -10x + 2x2 + -1(-5 + 1x + (-5 * x + x * x)) = 0 12 + -10x + 2x2 + -1(-5 + 1x + (-5x + x2)) = 0 Combine like terms: 1x + -5x = -4x 12 + -10x + 2x2 + -1(-5 + -4x + x2) = 0 12 + -10x + 2x2 + (-5 * -1 + -4x * -1 + x2 * -1) = 0 12 + -10x + 2x2 + (5 + 4x + -1x2) = 0 Reorder the terms: 12 + 5 + -10x + 4x + 2x2 + -1x2 = 0 Combine like terms: 12 + 5 = 17 17 + -10x + 4x + 2x2 + -1x2 = 0 Combine like terms: -10x + 4x = -6x 17 + -6x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 17 + -6x + 1x2 = 0 Solving 17 + -6x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -6x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -6x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -6x + x2 = 0 + -17 -6x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -6x + x2 = -17 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -17 + 9 Reorder the terms: 9 + -6x + x2 = -17 + 9 Combine like terms: -17 + 9 = -8 9 + -6x + x2 = -8 Factor a perfect square on the left side: (x + -3)(x + -3) = -8 Can't calculate square root of the right side. The solution to this equation could not be determined.
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