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