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Simplifying x4 + -29x2 + 54 = 0 Reorder the terms: 54 + -29x2 + x4 = 0 Solving 54 + -29x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (2 + -1x2)(27 + -1x2) = 0Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Subproblem 2
Set the factor '(27 + -1x2)' equal to zero and attempt to solve: Simplifying 27 + -1x2 = 0 Solving 27 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1x2 = 0 + -27 -1x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -1x2 = -27 Divide each side by '-1'. x2 = 27 Simplifying x2 = 27 Take the square root of each side: x = {-5.196152423, 5.196152423}Solution
x = {-1.414213562, 1.414213562, -5.196152423, 5.196152423}
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