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Simplifying z8 + -4z4 = 45 Reorder the terms: -4z4 + z8 = 45 Solving -4z4 + z8 = 45 Solving for variable 'z'. Reorder the terms: -45 + -4z4 + z8 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -4z4 + z8 = 0 Factor a trinomial. (-5 + -1z4)(9 + -1z4) = 0 Factor a difference between two squares. (-5 + -1z4)((3 + z2)(3 + -1z2)) = 0Subproblem 1
Set the factor '(-5 + -1z4)' equal to zero and attempt to solve: Simplifying -5 + -1z4 = 0 Solving -5 + -1z4 = 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 + -1z4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z4 = 0 + 5 -1z4 = 0 + 5 Combine like terms: 0 + 5 = 5 -1z4 = 5 Divide each side by '-1'. z4 = -5 Simplifying z4 = -5 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 + z2)' equal to zero and attempt to solve: Simplifying 3 + z2 = 0 Solving 3 + z2 = 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 + z2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z2 = 0 + -3 z2 = 0 + -3 Combine like terms: 0 + -3 = -3 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 3
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 Take the square root of each side: z = {-1.732050808, 1.732050808}Solution
z = {-1.732050808, 1.732050808}
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