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Simplifying s4 + 21s2 + -100 = 0 Reorder the terms: -100 + 21s2 + s4 = 0 Solving -100 + 21s2 + s4 = 0 Solving for variable 's'. Factor a trinomial. (-25 + -1s2)(4 + -1s2) = 0 Factor a difference between two squares. (-25 + -1s2)((2 + s)(2 + -1s)) = 0Subproblem 1
Set the factor '(-25 + -1s2)' equal to zero and attempt to solve: Simplifying -25 + -1s2 = 0 Solving -25 + -1s2 = 0 Move all terms containing s to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -1s2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1s2 = 0 + 25 -1s2 = 0 + 25 Combine like terms: 0 + 25 = 25 -1s2 = 25 Divide each side by '-1'. s2 = -25 Simplifying s2 = -25 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 '(2 + s)' equal to zero and attempt to solve: Simplifying 2 + s = 0 Solving 2 + s = 0 Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + s = 0 + -2 Combine like terms: 2 + -2 = 0 0 + s = 0 + -2 s = 0 + -2 Combine like terms: 0 + -2 = -2 s = -2 Simplifying s = -2Subproblem 3
Set the factor '(2 + -1s)' equal to zero and attempt to solve: Simplifying 2 + -1s = 0 Solving 2 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1s = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1s = 0 + -2 -1s = 0 + -2 Combine like terms: 0 + -2 = -2 -1s = -2 Divide each side by '-1'. s = 2 Simplifying s = 2Solution
s = {-2, 2}
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