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Simplifying x4 = -49 + 50x2 Solving x4 = -49 + 50x2 Solving for variable 'x'. Reorder the terms: 49 + -50x2 + x4 = -49 + 50x2 + 49 + -50x2 Reorder the terms: 49 + -50x2 + x4 = -49 + 49 + 50x2 + -50x2 Combine like terms: -49 + 49 = 0 49 + -50x2 + x4 = 0 + 50x2 + -50x2 49 + -50x2 + x4 = 50x2 + -50x2 Combine like terms: 50x2 + -50x2 = 0 49 + -50x2 + x4 = 0 Factor a trinomial. (1 + -1x2)(49 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(49 + -1x2) = 0 Factor a difference between two squares. ((7 + x)(7 + -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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 4
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-1, 1, -7, 7}
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