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Simplifying 3x(4x2 + -25)(x2 + 36) = 0 Reorder the terms: 3x(-25 + 4x2)(x2 + 36) = 0 Reorder the terms: 3x(-25 + 4x2)(36 + x2) = 0 Multiply (-25 + 4x2) * (36 + x2) 3x(-25(36 + x2) + 4x2 * (36 + x2)) = 0 3x((36 * -25 + x2 * -25) + 4x2 * (36 + x2)) = 0 3x((-900 + -25x2) + 4x2 * (36 + x2)) = 0 3x(-900 + -25x2 + (36 * 4x2 + x2 * 4x2)) = 0 3x(-900 + -25x2 + (144x2 + 4x4)) = 0 Combine like terms: -25x2 + 144x2 = 119x2 3x(-900 + 119x2 + 4x4) = 0 (-900 * 3x + 119x2 * 3x + 4x4 * 3x) = 0 (-2700x + 357x3 + 12x5) = 0 Solving -2700x + 357x3 + 12x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-900 + 119x2 + 4x4) = 0 Factor a trinomial. 3x((-36 + -1x2)(25 + -4x2)) = 0 Factor a difference between two squares. 3x((-36 + -1x2)((5 + 2x)(5 + -2x))) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-36 + -1x2)' equal to zero and attempt to solve: Simplifying -36 + -1x2 = 0 Solving -36 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + -1x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1x2 = 0 + 36 -1x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1x2 = 36 Divide each side by '-1'. x2 = -36 Simplifying x2 = -36 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 4
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {0, -2.5, 2.5}
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