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Simplifying (2x + 9)(x + 4) = x(2x + 7) Reorder the terms: (9 + 2x)(x + 4) = x(2x + 7) Reorder the terms: (9 + 2x)(4 + x) = x(2x + 7) Multiply (9 + 2x) * (4 + x) (9(4 + x) + 2x * (4 + x)) = x(2x + 7) ((4 * 9 + x * 9) + 2x * (4 + x)) = x(2x + 7) ((36 + 9x) + 2x * (4 + x)) = x(2x + 7) (36 + 9x + (4 * 2x + x * 2x)) = x(2x + 7) (36 + 9x + (8x + 2x2)) = x(2x + 7) Combine like terms: 9x + 8x = 17x (36 + 17x + 2x2) = x(2x + 7) Reorder the terms: 36 + 17x + 2x2 = x(7 + 2x) 36 + 17x + 2x2 = (7 * x + 2x * x) 36 + 17x + 2x2 = (7x + 2x2) Add '-2x2' to each side of the equation. 36 + 17x + 2x2 + -2x2 = 7x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 36 + 17x + 0 = 7x + 2x2 + -2x2 36 + 17x = 7x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 36 + 17x = 7x + 0 36 + 17x = 7x Solving 36 + 17x = 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. 36 + 17x + -7x = 7x + -7x Combine like terms: 17x + -7x = 10x 36 + 10x = 7x + -7x Combine like terms: 7x + -7x = 0 36 + 10x = 0 Add '-36' to each side of the equation. 36 + -36 + 10x = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 10x = 0 + -36 10x = 0 + -36 Combine like terms: 0 + -36 = -36 10x = -36 Divide each side by '10'. x = -3.6 Simplifying x = -3.6
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