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Simplifying (2x + 5)(x + 1) = 2x2 + 3x + 29 Reorder the terms: (5 + 2x)(x + 1) = 2x2 + 3x + 29 Reorder the terms: (5 + 2x)(1 + x) = 2x2 + 3x + 29 Multiply (5 + 2x) * (1 + x) (5(1 + x) + 2x * (1 + x)) = 2x2 + 3x + 29 ((1 * 5 + x * 5) + 2x * (1 + x)) = 2x2 + 3x + 29 ((5 + 5x) + 2x * (1 + x)) = 2x2 + 3x + 29 (5 + 5x + (1 * 2x + x * 2x)) = 2x2 + 3x + 29 (5 + 5x + (2x + 2x2)) = 2x2 + 3x + 29 Combine like terms: 5x + 2x = 7x (5 + 7x + 2x2) = 2x2 + 3x + 29 Reorder the terms: 5 + 7x + 2x2 = 29 + 3x + 2x2 Add '-2x2' to each side of the equation. 5 + 7x + 2x2 + -2x2 = 29 + 3x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + 7x + 0 = 29 + 3x + 2x2 + -2x2 5 + 7x = 29 + 3x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + 7x = 29 + 3x + 0 5 + 7x = 29 + 3x Solving 5 + 7x = 29 + 3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3x' to each side of the equation. 5 + 7x + -3x = 29 + 3x + -3x Combine like terms: 7x + -3x = 4x 5 + 4x = 29 + 3x + -3x Combine like terms: 3x + -3x = 0 5 + 4x = 29 + 0 5 + 4x = 29 Add '-5' to each side of the equation. 5 + -5 + 4x = 29 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 29 + -5 4x = 29 + -5 Combine like terms: 29 + -5 = 24 4x = 24 Divide each side by '4'. x = 6 Simplifying x = 6
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