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Simplifying (5x + 4)(5x + -4)(25x2 + 16) = 0 Reorder the terms: (4 + 5x)(5x + -4)(25x2 + 16) = 0 Reorder the terms: (4 + 5x)(-4 + 5x)(25x2 + 16) = 0 Reorder the terms: (4 + 5x)(-4 + 5x)(16 + 25x2) = 0 Multiply (4 + 5x) * (-4 + 5x) (4(-4 + 5x) + 5x * (-4 + 5x))(16 + 25x2) = 0 ((-4 * 4 + 5x * 4) + 5x * (-4 + 5x))(16 + 25x2) = 0 ((-16 + 20x) + 5x * (-4 + 5x))(16 + 25x2) = 0 (-16 + 20x + (-4 * 5x + 5x * 5x))(16 + 25x2) = 0 (-16 + 20x + (-20x + 25x2))(16 + 25x2) = 0 Combine like terms: 20x + -20x = 0 (-16 + 0 + 25x2)(16 + 25x2) = 0 (-16 + 25x2)(16 + 25x2) = 0 Multiply (-16 + 25x2) * (16 + 25x2) (-16(16 + 25x2) + 25x2 * (16 + 25x2)) = 0 ((16 * -16 + 25x2 * -16) + 25x2 * (16 + 25x2)) = 0 ((-256 + -400x2) + 25x2 * (16 + 25x2)) = 0 (-256 + -400x2 + (16 * 25x2 + 25x2 * 25x2)) = 0 (-256 + -400x2 + (400x2 + 625x4)) = 0 Combine like terms: -400x2 + 400x2 = 0 (-256 + 0 + 625x4) = 0 (-256 + 625x4) = 0 Solving -256 + 625x4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '256' to each side of the equation. -256 + 256 + 625x4 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 625x4 = 0 + 256 625x4 = 0 + 256 Combine like terms: 0 + 256 = 256 625x4 = 256 Divide each side by '625'. x4 = 0.4096 Simplifying x4 = 0.4096 Reorder the terms: -0.4096 + x4 = 0.4096 + -0.4096 Combine like terms: 0.4096 + -0.4096 = 0.0000 -0.4096 + x4 = 0.0000 Factor a difference between two squares. (0.64 + x2)(-0.64 + x2) = 0.0000 Factor a difference between two squares. (0.64 + x2)((0.8 + x)(-0.8 + x)) = 0.0000Subproblem 1
Set the factor '(0.64 + x2)' equal to zero and attempt to solve: Simplifying 0.64 + x2 = 0 Solving 0.64 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.64' to each side of the equation. 0.64 + -0.64 + x2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + x2 = 0 + -0.64 x2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 x2 = -0.64 Simplifying x2 = -0.64 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(0.8 + x)' equal to zero and attempt to solve: Simplifying 0.8 + x = 0 Solving 0.8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 0 + -0.8 x = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 x = -0.8 Simplifying x = -0.8Subproblem 3
Set the factor '(-0.8 + x)' equal to zero and attempt to solve: Simplifying -0.8 + x = 0 Solving -0.8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0 + 0.8 x = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 x = 0.8 Simplifying x = 0.8Solution
x = {-0.8, 0.8}
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