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Simplifying (4x + -2)(7x + 12) + (2 + -4x)(13 + -25x) = 0 Reorder the terms: (-2 + 4x)(7x + 12) + (2 + -4x)(13 + -25x) = 0 Reorder the terms: (-2 + 4x)(12 + 7x) + (2 + -4x)(13 + -25x) = 0 Multiply (-2 + 4x) * (12 + 7x) (-2(12 + 7x) + 4x * (12 + 7x)) + (2 + -4x)(13 + -25x) = 0 ((12 * -2 + 7x * -2) + 4x * (12 + 7x)) + (2 + -4x)(13 + -25x) = 0 ((-24 + -14x) + 4x * (12 + 7x)) + (2 + -4x)(13 + -25x) = 0 (-24 + -14x + (12 * 4x + 7x * 4x)) + (2 + -4x)(13 + -25x) = 0 (-24 + -14x + (48x + 28x2)) + (2 + -4x)(13 + -25x) = 0 Combine like terms: -14x + 48x = 34x (-24 + 34x + 28x2) + (2 + -4x)(13 + -25x) = 0 Multiply (2 + -4x) * (13 + -25x) -24 + 34x + 28x2 + (2(13 + -25x) + -4x * (13 + -25x)) = 0 -24 + 34x + 28x2 + ((13 * 2 + -25x * 2) + -4x * (13 + -25x)) = 0 -24 + 34x + 28x2 + ((26 + -50x) + -4x * (13 + -25x)) = 0 -24 + 34x + 28x2 + (26 + -50x + (13 * -4x + -25x * -4x)) = 0 -24 + 34x + 28x2 + (26 + -50x + (-52x + 100x2)) = 0 Combine like terms: -50x + -52x = -102x -24 + 34x + 28x2 + (26 + -102x + 100x2) = 0 Reorder the terms: -24 + 26 + 34x + -102x + 28x2 + 100x2 = 0 Combine like terms: -24 + 26 = 2 2 + 34x + -102x + 28x2 + 100x2 = 0 Combine like terms: 34x + -102x = -68x 2 + -68x + 28x2 + 100x2 = 0 Combine like terms: 28x2 + 100x2 = 128x2 2 + -68x + 128x2 = 0 Solving 2 + -68x + 128x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -34x + 64x2) = 0 Factor a trinomial. 2((1 + -32x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -32x)' equal to zero and attempt to solve: Simplifying 1 + -32x = 0 Solving 1 + -32x = 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 + -32x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -32x = 0 + -1 -32x = 0 + -1 Combine like terms: 0 + -1 = -1 -32x = -1 Divide each side by '-32'. x = 0.03125 Simplifying x = 0.03125Subproblem 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 = {0.03125, 0.5}
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