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Simplifying (x + -3)(2x + -5) + -1(x + 1)(x + -6) = 0 Reorder the terms: (-3 + x)(2x + -5) + -1(x + 1)(x + -6) = 0 Reorder the terms: (-3 + x)(-5 + 2x) + -1(x + 1)(x + -6) = 0 Multiply (-3 + x) * (-5 + 2x) (-3(-5 + 2x) + x(-5 + 2x)) + -1(x + 1)(x + -6) = 0 ((-5 * -3 + 2x * -3) + x(-5 + 2x)) + -1(x + 1)(x + -6) = 0 ((15 + -6x) + x(-5 + 2x)) + -1(x + 1)(x + -6) = 0 (15 + -6x + (-5 * x + 2x * x)) + -1(x + 1)(x + -6) = 0 (15 + -6x + (-5x + 2x2)) + -1(x + 1)(x + -6) = 0 Combine like terms: -6x + -5x = -11x (15 + -11x + 2x2) + -1(x + 1)(x + -6) = 0 Reorder the terms: 15 + -11x + 2x2 + -1(1 + x)(x + -6) = 0 Reorder the terms: 15 + -11x + 2x2 + -1(1 + x)(-6 + x) = 0 Multiply (1 + x) * (-6 + x) 15 + -11x + 2x2 + -1(1(-6 + x) + x(-6 + x)) = 0 15 + -11x + 2x2 + -1((-6 * 1 + x * 1) + x(-6 + x)) = 0 15 + -11x + 2x2 + -1((-6 + 1x) + x(-6 + x)) = 0 15 + -11x + 2x2 + -1(-6 + 1x + (-6 * x + x * x)) = 0 15 + -11x + 2x2 + -1(-6 + 1x + (-6x + x2)) = 0 Combine like terms: 1x + -6x = -5x 15 + -11x + 2x2 + -1(-6 + -5x + x2) = 0 15 + -11x + 2x2 + (-6 * -1 + -5x * -1 + x2 * -1) = 0 15 + -11x + 2x2 + (6 + 5x + -1x2) = 0 Reorder the terms: 15 + 6 + -11x + 5x + 2x2 + -1x2 = 0 Combine like terms: 15 + 6 = 21 21 + -11x + 5x + 2x2 + -1x2 = 0 Combine like terms: -11x + 5x = -6x 21 + -6x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 21 + -6x + 1x2 = 0 Solving 21 + -6x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -6x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -6x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -6x + x2 = 0 + -21 -6x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -6x + x2 = -21 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 = -21 + 9 Reorder the terms: 9 + -6x + x2 = -21 + 9 Combine like terms: -21 + 9 = -12 9 + -6x + x2 = -12 Factor a perfect square on the left side: (x + -3)(x + -3) = -12 Can't calculate square root of the right side. The solution to this equation could not be determined.
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