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Simplifying (5x + 3)(5x + -3)(25x2 + 9) = 0 Reorder the terms: (3 + 5x)(5x + -3)(25x2 + 9) = 0 Reorder the terms: (3 + 5x)(-3 + 5x)(25x2 + 9) = 0 Reorder the terms: (3 + 5x)(-3 + 5x)(9 + 25x2) = 0 Multiply (3 + 5x) * (-3 + 5x) (3(-3 + 5x) + 5x * (-3 + 5x))(9 + 25x2) = 0 ((-3 * 3 + 5x * 3) + 5x * (-3 + 5x))(9 + 25x2) = 0 ((-9 + 15x) + 5x * (-3 + 5x))(9 + 25x2) = 0 (-9 + 15x + (-3 * 5x + 5x * 5x))(9 + 25x2) = 0 (-9 + 15x + (-15x + 25x2))(9 + 25x2) = 0 Combine like terms: 15x + -15x = 0 (-9 + 0 + 25x2)(9 + 25x2) = 0 (-9 + 25x2)(9 + 25x2) = 0 Multiply (-9 + 25x2) * (9 + 25x2) (-9(9 + 25x2) + 25x2 * (9 + 25x2)) = 0 ((9 * -9 + 25x2 * -9) + 25x2 * (9 + 25x2)) = 0 ((-81 + -225x2) + 25x2 * (9 + 25x2)) = 0 (-81 + -225x2 + (9 * 25x2 + 25x2 * 25x2)) = 0 (-81 + -225x2 + (225x2 + 625x4)) = 0 Combine like terms: -225x2 + 225x2 = 0 (-81 + 0 + 625x4) = 0 (-81 + 625x4) = 0 Solving -81 + 625x4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81' to each side of the equation. -81 + 81 + 625x4 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 625x4 = 0 + 81 625x4 = 0 + 81 Combine like terms: 0 + 81 = 81 625x4 = 81 Divide each side by '625'. x4 = 0.1296 Simplifying x4 = 0.1296 Reorder the terms: -0.1296 + x4 = 0.1296 + -0.1296 Combine like terms: 0.1296 + -0.1296 = 0.0000 -0.1296 + x4 = 0.0000 Factor a difference between two squares. (0.36 + x2)(-0.36 + x2) = 0.0000 Factor a difference between two squares. (0.36 + x2)((0.6 + x)(-0.6 + x)) = 0.0000Subproblem 1
Set the factor '(0.36 + x2)' equal to zero and attempt to solve: Simplifying 0.36 + x2 = 0 Solving 0.36 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.36' to each side of the equation. 0.36 + -0.36 + x2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + x2 = 0 + -0.36 x2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 x2 = -0.36 Simplifying x2 = -0.36 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 '(0.6 + x)' equal to zero and attempt to solve: Simplifying 0.6 + x = 0 Solving 0.6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0 + -0.6 x = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 x = -0.6 Simplifying x = -0.6Subproblem 3
Set the factor '(-0.6 + x)' equal to zero and attempt to solve: Simplifying -0.6 + x = 0 Solving -0.6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0 + 0.6 x = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 x = 0.6 Simplifying x = 0.6Solution
x = {-0.6, 0.6}
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