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Simplifying 16x4 = 41x2 + -25 Reorder the terms: 16x4 = -25 + 41x2 Solving 16x4 = -25 + 41x2 Solving for variable 'x'. Reorder the terms: 25 + -41x2 + 16x4 = -25 + 41x2 + 25 + -41x2 Reorder the terms: 25 + -41x2 + 16x4 = -25 + 25 + 41x2 + -41x2 Combine like terms: -25 + 25 = 0 25 + -41x2 + 16x4 = 0 + 41x2 + -41x2 25 + -41x2 + 16x4 = 41x2 + -41x2 Combine like terms: 41x2 + -41x2 = 0 25 + -41x2 + 16x4 = 0 Factor a trinomial. (1 + -1x2)(25 + -16x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(25 + -16x2) = 0 Factor a difference between two squares. ((5 + 4x)(5 + -4x))(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 '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 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 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25Subproblem 4
Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Solution
x = {-1, 1, -1.25, 1.25}
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