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Simplifying x4 = 22x2 + 75 Reorder the terms: x4 = 75 + 22x2 Solving x4 = 75 + 22x2 Solving for variable 'x'. Reorder the terms: -75 + -22x2 + x4 = 75 + 22x2 + -75 + -22x2 Reorder the terms: -75 + -22x2 + x4 = 75 + -75 + 22x2 + -22x2 Combine like terms: 75 + -75 = 0 -75 + -22x2 + x4 = 0 + 22x2 + -22x2 -75 + -22x2 + x4 = 22x2 + -22x2 Combine like terms: 22x2 + -22x2 = 0 -75 + -22x2 + x4 = 0 Factor a trinomial. (-3 + -1x2)(25 + -1x2) = 0 Factor a difference between two squares. (-3 + -1x2)((5 + x)(5 + -1x)) = 0Subproblem 1
Set the factor '(-3 + -1x2)' equal to zero and attempt to solve: Simplifying -3 + -1x2 = 0 Solving -3 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x2 = 0 + 3 -1x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x2 = 3 Divide each side by '-1'. x2 = -3 Simplifying x2 = -3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.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 = {-5, 5}
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