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Simplifying -60z5 + 16z + 12z3 = 0 Reorder the terms: 16z + 12z3 + -60z5 = 0 Solving 16z + 12z3 + -60z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z'. 4z(4 + 3z2 + -15z4) = 0 Ignore the factor 4.Subproblem 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 '(4 + 3z2 + -15z4)' equal to zero and attempt to solve: Simplifying 4 + 3z2 + -15z4 = 0 Solving 4 + 3z2 + -15z4 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.2666666667 + -0.2z2 + z4 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + -0.2z2 + 0.2666666667 + z4 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + -0.2z2 + z4 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + -0.2z2 + z4 = 0 + 0.2666666667 -0.2z2 + z4 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 -0.2z2 + z4 = 0.2666666667 The z term is -0.2z2. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2z2 + 0.01 + z4 = 0.2666666667 + 0.01 Reorder the terms: 0.01 + -0.2z2 + z4 = 0.2666666667 + 0.01 Combine like terms: 0.2666666667 + 0.01 = 0.2766666667 0.01 + -0.2z2 + z4 = 0.2766666667 Factor a perfect square on the left side: (z2 + -0.1)(z2 + -0.1) = 0.2766666667 Calculate the square root of the right side: 0.525991128 Break this problem into two subproblems by setting (z2 + -0.1) equal to 0.525991128 and -0.525991128.Subproblem 1
z2 + -0.1 = 0.525991128 Simplifying z2 + -0.1 = 0.525991128 Reorder the terms: -0.1 + z2 = 0.525991128 Solving -0.1 + z2 = 0.525991128 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + z2 = 0.525991128 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + z2 = 0.525991128 + 0.1 z2 = 0.525991128 + 0.1 Combine like terms: 0.525991128 + 0.1 = 0.625991128 z2 = 0.625991128 Simplifying z2 = 0.625991128 Take the square root of each side: z = {-0.791196011, 0.791196011}Subproblem 2
z2 + -0.1 = -0.525991128 Simplifying z2 + -0.1 = -0.525991128 Reorder the terms: -0.1 + z2 = -0.525991128 Solving -0.1 + z2 = -0.525991128 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + z2 = -0.525991128 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + z2 = -0.525991128 + 0.1 z2 = -0.525991128 + 0.1 Combine like terms: -0.525991128 + 0.1 = -0.425991128 z2 = -0.425991128 Simplifying z2 = -0.425991128 Reorder the terms: 0.425991128 + z2 = -0.425991128 + 0.425991128 Combine like terms: -0.425991128 + 0.425991128 = 0.000000000 0.425991128 + z2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
z = {0}
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