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Simplifying 0 = x4 + -41x2 + 400 Reorder the terms: 0 = 400 + -41x2 + x4 Solving 0 = 400 + -41x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -400 = -400 -400 + 41x2 + -1x4 = 400 + -41x2 + x4 + -400 + 41x2 + -1x4 Reorder the terms: -400 + 41x2 + -1x4 = 400 + -400 + -41x2 + 41x2 + x4 + -1x4 Combine like terms: 400 + -400 = 0 -400 + 41x2 + -1x4 = 0 + -41x2 + 41x2 + x4 + -1x4 -400 + 41x2 + -1x4 = -41x2 + 41x2 + x4 + -1x4 Combine like terms: -41x2 + 41x2 = 0 -400 + 41x2 + -1x4 = 0 + x4 + -1x4 -400 + 41x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -400 + 41x2 + -1x4 = 0 Factor a trinomial. (-25 + x2)(16 + -1x2) = 0 Factor a difference between two squares. ((5 + x)(-5 + x))(16 + -1x2) = 0 Factor a difference between two squares. ((4 + x)(4 + -1x))(5 + x)(-5 + x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 4
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-5, 5, -4, 4}
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