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Simplifying 2x4 + -54x2 = -100 Reorder the terms: -54x2 + 2x4 = -100 Solving -54x2 + 2x4 = -100 Solving for variable 'x'. Reorder the terms: 100 + -54x2 + 2x4 = -100 + 100 Combine like terms: -100 + 100 = 0 100 + -54x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -27x2 + x4) = 0 Factor a trinomial. 2((2 + -1x2)(25 + -1x2)) = 0 Factor a difference between two squares. 2((2 + -1x2)((5 + x)(5 + -1x))) = 0 Ignore the factor 2.Subproblem 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 '(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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-1.414213562, 1.414213562, -5, 5}
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