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Simplifying 2x4 + -20x2 + 50 = 0 Reorder the terms: 50 + -20x2 + 2x4 = 0 Solving 50 + -20x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -10x2 + x4) = 0 Factor a trinomial. 2((5 + -1x2)(5 + -1x2)) = 0 Ignore the factor 2.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 '(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}Solution
x = {-2.236067978, 2.236067978, -2.236067978, 2.236067978}
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