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Simplifying (x + 5)(2x + 5) = -5 Reorder the terms: (5 + x)(2x + 5) = -5 Reorder the terms: (5 + x)(5 + 2x) = -5 Multiply (5 + x) * (5 + 2x) (5(5 + 2x) + x(5 + 2x)) = -5 ((5 * 5 + 2x * 5) + x(5 + 2x)) = -5 ((25 + 10x) + x(5 + 2x)) = -5 (25 + 10x + (5 * x + 2x * x)) = -5 (25 + 10x + (5x + 2x2)) = -5 Combine like terms: 10x + 5x = 15x (25 + 15x + 2x2) = -5 Solving 25 + 15x + 2x2 = -5 Solving for variable 'x'. Reorder the terms: 25 + 5 + 15x + 2x2 = -5 + 5 Combine like terms: 25 + 5 = 30 30 + 15x + 2x2 = -5 + 5 Combine like terms: -5 + 5 = 0 30 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15 + 7.5x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + 7.5x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 7.5x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 7.5x + x2 = 0 + -15 7.5x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 7.5x + x2 = -15 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -15 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -15 + 14.0625 Combine like terms: -15 + 14.0625 = -0.9375 14.0625 + 7.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = -0.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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