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Simplifying (x + -2)(2x + -3) + -1(x + 1)(x + -6) = 0 Reorder the terms: (-2 + x)(2x + -3) + -1(x + 1)(x + -6) = 0 Reorder the terms: (-2 + x)(-3 + 2x) + -1(x + 1)(x + -6) = 0 Multiply (-2 + x) * (-3 + 2x) (-2(-3 + 2x) + x(-3 + 2x)) + -1(x + 1)(x + -6) = 0 ((-3 * -2 + 2x * -2) + x(-3 + 2x)) + -1(x + 1)(x + -6) = 0 ((6 + -4x) + x(-3 + 2x)) + -1(x + 1)(x + -6) = 0 (6 + -4x + (-3 * x + 2x * x)) + -1(x + 1)(x + -6) = 0 (6 + -4x + (-3x + 2x2)) + -1(x + 1)(x + -6) = 0 Combine like terms: -4x + -3x = -7x (6 + -7x + 2x2) + -1(x + 1)(x + -6) = 0 Reorder the terms: 6 + -7x + 2x2 + -1(1 + x)(x + -6) = 0 Reorder the terms: 6 + -7x + 2x2 + -1(1 + x)(-6 + x) = 0 Multiply (1 + x) * (-6 + x) 6 + -7x + 2x2 + -1(1(-6 + x) + x(-6 + x)) = 0 6 + -7x + 2x2 + -1((-6 * 1 + x * 1) + x(-6 + x)) = 0 6 + -7x + 2x2 + -1((-6 + 1x) + x(-6 + x)) = 0 6 + -7x + 2x2 + -1(-6 + 1x + (-6 * x + x * x)) = 0 6 + -7x + 2x2 + -1(-6 + 1x + (-6x + x2)) = 0 Combine like terms: 1x + -6x = -5x 6 + -7x + 2x2 + -1(-6 + -5x + x2) = 0 6 + -7x + 2x2 + (-6 * -1 + -5x * -1 + x2 * -1) = 0 6 + -7x + 2x2 + (6 + 5x + -1x2) = 0 Reorder the terms: 6 + 6 + -7x + 5x + 2x2 + -1x2 = 0 Combine like terms: 6 + 6 = 12 12 + -7x + 5x + 2x2 + -1x2 = 0 Combine like terms: -7x + 5x = -2x 12 + -2x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 12 + -2x + 1x2 = 0 Solving 12 + -2x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -2x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -2x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -2x + x2 = 0 + -12 -2x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -2x + x2 = -12 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -12 + 1 Reorder the terms: 1 + -2x + x2 = -12 + 1 Combine like terms: -12 + 1 = -11 1 + -2x + x2 = -11 Factor a perfect square on the left side: (x + -1)(x + -1) = -11 Can't calculate square root of the right side. The solution to this equation could not be determined.
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