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Simplifying 3x4 + -54x2 + 195 = 0 Reorder the terms: 195 + -54x2 + 3x4 = 0 Solving 195 + -54x2 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(65 + -18x2 + x4) = 0 Factor a trinomial. 3((5 + -1x2)(13 + -1x2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -1x2 = 0 Solving 5 + -1x2 = 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 + -1x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x2 = 0 + -5 -1x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1x2 = -5 Divide each side by '-1'. x2 = 5 Simplifying x2 = 5 Take the square root of each side: x = {-2.236067978, 2.236067978}Subproblem 2
Set the factor '(13 + -1x2)' equal to zero and attempt to solve: Simplifying 13 + -1x2 = 0 Solving 13 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x2 = 0 + -13 -1x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -1x2 = -13 Divide each side by '-1'. x2 = 13 Simplifying x2 = 13 Take the square root of each side: x = {-3.605551275, 3.605551275}Solution
x = {-2.236067978, 2.236067978, -3.605551275, 3.605551275}
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