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Simplifying z5 + -49z = 0 Reorder the terms: -49z + z5 = 0 Solving -49z + z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-49 + z4) = 0 Factor a difference between two squares. z((7 + z2)(-7 + z2)) = 0Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(7 + z2)' equal to zero and attempt to solve: Simplifying 7 + z2 = 0 Solving 7 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z2 = 0 + -7 z2 = 0 + -7 Combine like terms: 0 + -7 = -7 z2 = -7 Simplifying z2 = -7 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 '(-7 + z2)' equal to zero and attempt to solve: Simplifying -7 + z2 = 0 Solving -7 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + z2 = 0 + 7 z2 = 0 + 7 Combine like terms: 0 + 7 = 7 z2 = 7 Simplifying z2 = 7 Take the square root of each side: z = {-2.645751311, 2.645751311}Solution
z = {0, -2.645751311, 2.645751311}
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