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Simplifying x4 + 6x2 + -7 = 0 Reorder the terms: -7 + 6x2 + x4 = 0 Solving -7 + 6x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -1x2)(1 + -1x2) = 0 Factor a difference between two squares. (-7 + -1x2)((1 + x)(1 + -1x)) = 0Subproblem 1
Set the factor '(-7 + -1x2)' equal to zero and attempt to solve: Simplifying -7 + -1x2 = 0 Solving -7 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x2 = 0 + 7 -1x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1x2 = 7 Divide each side by '-1'. x2 = -7 Simplifying x2 = -7 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-1, 1}
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