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Simplifying (x + 5)(x + 6) = x + 5x + 6 Reorder the terms: (5 + x)(x + 6) = x + 5x + 6 Reorder the terms: (5 + x)(6 + x) = x + 5x + 6 Multiply (5 + x) * (6 + x) (5(6 + x) + x(6 + x)) = x + 5x + 6 ((6 * 5 + x * 5) + x(6 + x)) = x + 5x + 6 ((30 + 5x) + x(6 + x)) = x + 5x + 6 (30 + 5x + (6 * x + x * x)) = x + 5x + 6 (30 + 5x + (6x + x2)) = x + 5x + 6 Combine like terms: 5x + 6x = 11x (30 + 11x + x2) = x + 5x + 6 Reorder the terms: 30 + 11x + x2 = 6 + x + 5x Combine like terms: x + 5x = 6x 30 + 11x + x2 = 6 + 6x Solving 30 + 11x + x2 = 6 + 6x Solving for variable 'x'. Reorder the terms: 30 + -6 + 11x + -6x + x2 = 6 + 6x + -6 + -6x Combine like terms: 30 + -6 = 24 24 + 11x + -6x + x2 = 6 + 6x + -6 + -6x Combine like terms: 11x + -6x = 5x 24 + 5x + x2 = 6 + 6x + -6 + -6x Reorder the terms: 24 + 5x + x2 = 6 + -6 + 6x + -6x Combine like terms: 6 + -6 = 0 24 + 5x + x2 = 0 + 6x + -6x 24 + 5x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 24 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 5x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 5x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 5x + x2 = 0 + -24 5x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 5x + x2 = -24 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -24 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -24 + 6.25 Combine like terms: -24 + 6.25 = -17.75 6.25 + 5x + x2 = -17.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -17.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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