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Simplifying x4 + -20x2 = -75 Reorder the terms: -20x2 + x4 = -75 Solving -20x2 + x4 = -75 Solving for variable 'x'. Reorder the terms: 75 + -20x2 + x4 = -75 + 75 Combine like terms: -75 + 75 = 0 75 + -20x2 + x4 = 0 Factor a trinomial. (5 + -1x2)(15 + -1x2) = 0Subproblem 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 '(15 + -1x2)' equal to zero and attempt to solve: Simplifying 15 + -1x2 = 0 Solving 15 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x2 = 0 + -15 -1x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -1x2 = -15 Divide each side by '-1'. x2 = 15 Simplifying x2 = 15 Take the square root of each side: x = {-3.872983346, 3.872983346}Solution
x = {-2.236067978, 2.236067978, -3.872983346, 3.872983346}
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