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Simplifying z8 + -22z4 = 75 Reorder the terms: -22z4 + z8 = 75 Solving -22z4 + z8 = 75 Solving for variable 'z'. Reorder the terms: -75 + -22z4 + z8 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + -22z4 + z8 = 0 Factor a trinomial. (-3 + -1z4)(25 + -1z4) = 0 Factor a difference between two squares. (-3 + -1z4)((5 + z2)(5 + -1z2)) = 0Subproblem 1
Set the factor '(-3 + -1z4)' equal to zero and attempt to solve: Simplifying -3 + -1z4 = 0 Solving -3 + -1z4 = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1z4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z4 = 0 + 3 -1z4 = 0 + 3 Combine like terms: 0 + 3 = 3 -1z4 = 3 Divide each side by '-1'. z4 = -3 Simplifying z4 = -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 + z2)' equal to zero and attempt to solve: Simplifying 5 + z2 = 0 Solving 5 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z2 = 0 + -5 z2 = 0 + -5 Combine like terms: 0 + -5 = -5 z2 = -5 Simplifying z2 = -5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(5 + -1z2)' equal to zero and attempt to solve: Simplifying 5 + -1z2 = 0 Solving 5 + -1z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1z2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1z2 = 0 + -5 -1z2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1z2 = -5 Divide each side by '-1'. z2 = 5 Simplifying z2 = 5 Take the square root of each side: z = {-2.236067978, 2.236067978}Solution
z = {-2.236067978, 2.236067978}
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