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Simplifying z4 = 6z2 + 27 Reorder the terms: z4 = 27 + 6z2 Solving z4 = 27 + 6z2 Solving for variable 'z'. Reorder the terms: -27 + -6z2 + z4 = 27 + 6z2 + -27 + -6z2 Reorder the terms: -27 + -6z2 + z4 = 27 + -27 + 6z2 + -6z2 Combine like terms: 27 + -27 = 0 -27 + -6z2 + z4 = 0 + 6z2 + -6z2 -27 + -6z2 + z4 = 6z2 + -6z2 Combine like terms: 6z2 + -6z2 = 0 -27 + -6z2 + z4 = 0 Factor a trinomial. (-3 + -1z2)(9 + -1z2) = 0 Factor a difference between two squares. (-3 + -1z2)((3 + z)(3 + -1z)) = 0Subproblem 1
Set the factor '(-3 + -1z2)' equal to zero and attempt to solve: Simplifying -3 + -1z2 = 0 Solving -3 + -1z2 = 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 + -1z2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z2 = 0 + 3 -1z2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1z2 = 3 Divide each side by '-1'. z2 = -3 Simplifying z2 = -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 '(3 + z)' equal to zero and attempt to solve: Simplifying 3 + z = 0 Solving 3 + z = 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 + z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z = 0 + -3 z = 0 + -3 Combine like terms: 0 + -3 = -3 z = -3 Simplifying z = -3Subproblem 3
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 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 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {-3, 3}
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