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Simplifying (10x + 5)(4x + 4) = (9x + 7.5)(2x + 4) Reorder the terms: (5 + 10x)(4x + 4) = (9x + 7.5)(2x + 4) Reorder the terms: (5 + 10x)(4 + 4x) = (9x + 7.5)(2x + 4) Multiply (5 + 10x) * (4 + 4x) (5(4 + 4x) + 10x * (4 + 4x)) = (9x + 7.5)(2x + 4) ((4 * 5 + 4x * 5) + 10x * (4 + 4x)) = (9x + 7.5)(2x + 4) ((20 + 20x) + 10x * (4 + 4x)) = (9x + 7.5)(2x + 4) (20 + 20x + (4 * 10x + 4x * 10x)) = (9x + 7.5)(2x + 4) (20 + 20x + (40x + 40x2)) = (9x + 7.5)(2x + 4) Combine like terms: 20x + 40x = 60x (20 + 60x + 40x2) = (9x + 7.5)(2x + 4) Reorder the terms: 20 + 60x + 40x2 = (7.5 + 9x)(2x + 4) Reorder the terms: 20 + 60x + 40x2 = (7.5 + 9x)(4 + 2x) Multiply (7.5 + 9x) * (4 + 2x) 20 + 60x + 40x2 = (7.5(4 + 2x) + 9x * (4 + 2x)) 20 + 60x + 40x2 = ((4 * 7.5 + 2x * 7.5) + 9x * (4 + 2x)) 20 + 60x + 40x2 = ((30 + 15x) + 9x * (4 + 2x)) 20 + 60x + 40x2 = (30 + 15x + (4 * 9x + 2x * 9x)) 20 + 60x + 40x2 = (30 + 15x + (36x + 18x2)) Combine like terms: 15x + 36x = 51x 20 + 60x + 40x2 = (30 + 51x + 18x2) Solving 20 + 60x + 40x2 = 30 + 51x + 18x2 Solving for variable 'x'. Reorder the terms: 20 + -30 + 60x + -51x + 40x2 + -18x2 = 30 + 51x + 18x2 + -30 + -51x + -18x2 Combine like terms: 20 + -30 = -10 -10 + 60x + -51x + 40x2 + -18x2 = 30 + 51x + 18x2 + -30 + -51x + -18x2 Combine like terms: 60x + -51x = 9x -10 + 9x + 40x2 + -18x2 = 30 + 51x + 18x2 + -30 + -51x + -18x2 Combine like terms: 40x2 + -18x2 = 22x2 -10 + 9x + 22x2 = 30 + 51x + 18x2 + -30 + -51x + -18x2 Reorder the terms: -10 + 9x + 22x2 = 30 + -30 + 51x + -51x + 18x2 + -18x2 Combine like terms: 30 + -30 = 0 -10 + 9x + 22x2 = 0 + 51x + -51x + 18x2 + -18x2 -10 + 9x + 22x2 = 51x + -51x + 18x2 + -18x2 Combine like terms: 51x + -51x = 0 -10 + 9x + 22x2 = 0 + 18x2 + -18x2 -10 + 9x + 22x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -10 + 9x + 22x2 = 0 Factor a trinomial. (-10 + -11x)(1 + -2x) = 0Subproblem 1
Set the factor '(-10 + -11x)' equal to zero and attempt to solve: Simplifying -10 + -11x = 0 Solving -10 + -11x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -11x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -11x = 0 + 10 -11x = 0 + 10 Combine like terms: 0 + 10 = 10 -11x = 10 Divide each side by '-11'. x = -0.9090909091 Simplifying x = -0.9090909091Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-0.9090909091, 0.5}
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