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Simplifying (z4) + -1(8z2) = 0 z4 + -1(8z2) = 0 Remove parenthesis around (8z2) z4 + -1 * 8z2 = 0 Multiply -1 * 8 z4 + -8z2 = 0 Reorder the terms: -8z2 + z4 = 0 Solving -8z2 + z4 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z2'. z2(-8 + z2) = 0Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}Subproblem 2
Set the factor '(-8 + z2)' equal to zero and attempt to solve: Simplifying -8 + z2 = 0 Solving -8 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + z2 = 0 + 8 z2 = 0 + 8 Combine like terms: 0 + 8 = 8 z2 = 8 Simplifying z2 = 8 Take the square root of each side: z = {-2.828427125, 2.828427125}Solution
z = {0, -2.828427125, 2.828427125}
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