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Simplifying 54x2 + x4 = 1120 Solving 54x2 + x4 = 1120 Solving for variable 'x'. Reorder the terms: -1120 + 54x2 + x4 = 1120 + -1120 Combine like terms: 1120 + -1120 = 0 -1120 + 54x2 + x4 = 0 Factor a trinomial. (-70 + -1x2)(16 + -1x2) = 0 Factor a difference between two squares. (-70 + -1x2)((4 + x)(4 + -1x)) = 0Subproblem 1
Set the factor '(-70 + -1x2)' equal to zero and attempt to solve: Simplifying -70 + -1x2 = 0 Solving -70 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + -1x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -1x2 = 0 + 70 -1x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -1x2 = 70 Divide each side by '-1'. x2 = -70 Simplifying x2 = -70 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-4, 4}
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