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Simplifying z4 + -11z2 + 30 = 0 Reorder the terms: 30 + -11z2 + z4 = 0 Solving 30 + -11z2 + z4 = 0 Solving for variable 'z'. Factor a trinomial. (5 + -1z2)(6 + -1z2) = 0Subproblem 1
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}Subproblem 2
Set the factor '(6 + -1z2)' equal to zero and attempt to solve: Simplifying 6 + -1z2 = 0 Solving 6 + -1z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1z2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1z2 = 0 + -6 -1z2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1z2 = -6 Divide each side by '-1'. z2 = 6 Simplifying z2 = 6 Take the square root of each side: z = {-2.449489743, 2.449489743}Solution
z = {-2.236067978, 2.236067978, -2.449489743, 2.449489743}
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