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Simplifying (2x + 1)(2x + 1) + (x + 2)(x + 2) + -1x(5x + 13) = 0 Reorder the terms: (1 + 2x)(2x + 1) + (x + 2)(x + 2) + -1x(5x + 13) = 0 Reorder the terms: (1 + 2x)(1 + 2x) + (x + 2)(x + 2) + -1x(5x + 13) = 0 Multiply (1 + 2x) * (1 + 2x) (1(1 + 2x) + 2x * (1 + 2x)) + (x + 2)(x + 2) + -1x(5x + 13) = 0 ((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + (x + 2)(x + 2) + -1x(5x + 13) = 0 ((1 + 2x) + 2x * (1 + 2x)) + (x + 2)(x + 2) + -1x(5x + 13) = 0 (1 + 2x + (1 * 2x + 2x * 2x)) + (x + 2)(x + 2) + -1x(5x + 13) = 0 (1 + 2x + (2x + 4x2)) + (x + 2)(x + 2) + -1x(5x + 13) = 0 Combine like terms: 2x + 2x = 4x (1 + 4x + 4x2) + (x + 2)(x + 2) + -1x(5x + 13) = 0 Reorder the terms: 1 + 4x + 4x2 + (2 + x)(x + 2) + -1x(5x + 13) = 0 Reorder the terms: 1 + 4x + 4x2 + (2 + x)(2 + x) + -1x(5x + 13) = 0 Multiply (2 + x) * (2 + x) 1 + 4x + 4x2 + (2(2 + x) + x(2 + x)) + -1x(5x + 13) = 0 1 + 4x + 4x2 + ((2 * 2 + x * 2) + x(2 + x)) + -1x(5x + 13) = 0 1 + 4x + 4x2 + ((4 + 2x) + x(2 + x)) + -1x(5x + 13) = 0 1 + 4x + 4x2 + (4 + 2x + (2 * x + x * x)) + -1x(5x + 13) = 0 1 + 4x + 4x2 + (4 + 2x + (2x + x2)) + -1x(5x + 13) = 0 Combine like terms: 2x + 2x = 4x 1 + 4x + 4x2 + (4 + 4x + x2) + -1x(5x + 13) = 0 Reorder the terms: 1 + 4x + 4x2 + 4 + 4x + x2 + -1x(13 + 5x) = 0 1 + 4x + 4x2 + 4 + 4x + x2 + (13 * -1x + 5x * -1x) = 0 1 + 4x + 4x2 + 4 + 4x + x2 + (-13x + -5x2) = 0 Reorder the terms: 1 + 4 + 4x + 4x + -13x + 4x2 + x2 + -5x2 = 0 Combine like terms: 1 + 4 = 5 5 + 4x + 4x + -13x + 4x2 + x2 + -5x2 = 0 Combine like terms: 4x + 4x = 8x 5 + 8x + -13x + 4x2 + x2 + -5x2 = 0 Combine like terms: 8x + -13x = -5x 5 + -5x + 4x2 + x2 + -5x2 = 0 Combine like terms: 4x2 + x2 = 5x2 5 + -5x + 5x2 + -5x2 = 0 Combine like terms: 5x2 + -5x2 = 0 5 + -5x + 0 = 0 5 + -5x = 0 Solving 5 + -5x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -5x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5x = 0 + -5 -5x = 0 + -5 Combine like terms: 0 + -5 = -5 -5x = -5 Divide each side by '-5'. x = 1 Simplifying x = 1
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