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Simplifying x4 + -90x2 + 3x + 739 = 3x + 10 Reorder the terms: 739 + 3x + -90x2 + x4 = 3x + 10 Reorder the terms: 739 + 3x + -90x2 + x4 = 10 + 3x Add '-3x' to each side of the equation. 739 + 3x + -90x2 + -3x + x4 = 10 + 3x + -3x Reorder the terms: 739 + 3x + -3x + -90x2 + x4 = 10 + 3x + -3x Combine like terms: 3x + -3x = 0 739 + 0 + -90x2 + x4 = 10 + 3x + -3x 739 + -90x2 + x4 = 10 + 3x + -3x Combine like terms: 3x + -3x = 0 739 + -90x2 + x4 = 10 + 0 739 + -90x2 + x4 = 10 Solving 739 + -90x2 + x4 = 10 Solving for variable 'x'. Reorder the terms: 739 + -10 + -90x2 + x4 = 10 + -10 Combine like terms: 739 + -10 = 729 729 + -90x2 + x4 = 10 + -10 Combine like terms: 10 + -10 = 0 729 + -90x2 + x4 = 0 Factor a trinomial. (9 + -1x2)(81 + -1x2) = 0 Factor a difference between two squares. ((3 + x)(3 + -1x))(81 + -1x2) = 0 Factor a difference between two squares. ((9 + x)(9 + -1x))(3 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 3
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 4
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-3, 3, -9, 9}
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