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Simplifying (2x + 3)(x + 5) = (x + -3) * 2 Reorder the terms: (3 + 2x)(x + 5) = (x + -3) * 2 Reorder the terms: (3 + 2x)(5 + x) = (x + -3) * 2 Multiply (3 + 2x) * (5 + x) (3(5 + x) + 2x * (5 + x)) = (x + -3) * 2 ((5 * 3 + x * 3) + 2x * (5 + x)) = (x + -3) * 2 ((15 + 3x) + 2x * (5 + x)) = (x + -3) * 2 (15 + 3x + (5 * 2x + x * 2x)) = (x + -3) * 2 (15 + 3x + (10x + 2x2)) = (x + -3) * 2 Combine like terms: 3x + 10x = 13x (15 + 13x + 2x2) = (x + -3) * 2 Reorder the terms: 15 + 13x + 2x2 = (-3 + x) * 2 Reorder the terms for easier multiplication: 15 + 13x + 2x2 = 2(-3 + x) 15 + 13x + 2x2 = (-3 * 2 + x * 2) 15 + 13x + 2x2 = (-6 + 2x) Solving 15 + 13x + 2x2 = -6 + 2x Solving for variable 'x'. Reorder the terms: 15 + 6 + 13x + -2x + 2x2 = -6 + 2x + 6 + -2x Combine like terms: 15 + 6 = 21 21 + 13x + -2x + 2x2 = -6 + 2x + 6 + -2x Combine like terms: 13x + -2x = 11x 21 + 11x + 2x2 = -6 + 2x + 6 + -2x Reorder the terms: 21 + 11x + 2x2 = -6 + 6 + 2x + -2x Combine like terms: -6 + 6 = 0 21 + 11x + 2x2 = 0 + 2x + -2x 21 + 11x + 2x2 = 2x + -2x Combine like terms: 2x + -2x = 0 21 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + 5.5x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + 5.5x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + 5.5x + x2 = 0 + -10.5 5.5x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 5.5x + x2 = -10.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -10.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -10.5 + 7.5625 Combine like terms: -10.5 + 7.5625 = -2.9375 7.5625 + 5.5x + x2 = -2.9375 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = -2.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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