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Simplifying x4 = 65x2 + -64 Reorder the terms: x4 = -64 + 65x2 Solving x4 = -64 + 65x2 Solving for variable 'x'. Reorder the terms: 64 + -65x2 + x4 = -64 + 65x2 + 64 + -65x2 Reorder the terms: 64 + -65x2 + x4 = -64 + 64 + 65x2 + -65x2 Combine like terms: -64 + 64 = 0 64 + -65x2 + x4 = 0 + 65x2 + -65x2 64 + -65x2 + x4 = 65x2 + -65x2 Combine like terms: 65x2 + -65x2 = 0 64 + -65x2 + x4 = 0 Factor a trinomial. (1 + -1x2)(64 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(64 + -1x2) = 0 Factor a difference between two squares. ((8 + x)(8 + -1x))(1 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 3
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 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 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 4
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 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 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-1, 1, -8, 8}
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