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Simplifying 4x4 + -48x2 + 128 = 0 Reorder the terms: 128 + -48x2 + 4x4 = 0 Solving 128 + -48x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(32 + -12x2 + x4) = 0 Factor a trinomial. 4((4 + -1x2)(8 + -1x2)) = 0 Factor a difference between two squares. 4(((2 + x)(2 + -1x))(8 + -1x2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + -1x2)' equal to zero and attempt to solve: Simplifying 8 + -1x2 = 0 Solving 8 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x2 = 0 + -8 -1x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1x2 = -8 Divide each side by '-1'. x2 = 8 Simplifying x2 = 8 Take the square root of each side: x = {-2.828427125, 2.828427125}Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-2.828427125, 2.828427125, -2, 2}
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