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Simplifying 19z8 + 10z5 + -13z2 = 0 Reorder the terms: -13z2 + 10z5 + 19z8 = 0 Solving -13z2 + 10z5 + 19z8 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z2'. z2(-13 + 10z3 + 19z6) = 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 '(-13 + 10z3 + 19z6)' equal to zero and attempt to solve: Simplifying -13 + 10z3 + 19z6 = 0 Solving -13 + 10z3 + 19z6 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.6842105263 + 0.5263157895z3 + z6 = 0 Move the constant term to the right: Add '0.6842105263' to each side of the equation. -0.6842105263 + 0.5263157895z3 + 0.6842105263 + z6 = 0 + 0.6842105263 Reorder the terms: -0.6842105263 + 0.6842105263 + 0.5263157895z3 + z6 = 0 + 0.6842105263 Combine like terms: -0.6842105263 + 0.6842105263 = 0.0000000000 0.0000000000 + 0.5263157895z3 + z6 = 0 + 0.6842105263 0.5263157895z3 + z6 = 0 + 0.6842105263 Combine like terms: 0 + 0.6842105263 = 0.6842105263 0.5263157895z3 + z6 = 0.6842105263 The z term is 0.5263157895z3. Take half its coefficient (0.2631578948). Square it (0.06925207760) and add it to both sides. Add '0.06925207760' to each side of the equation. 0.5263157895z3 + 0.06925207760 + z6 = 0.6842105263 + 0.06925207760 Reorder the terms: 0.06925207760 + 0.5263157895z3 + z6 = 0.6842105263 + 0.06925207760 Combine like terms: 0.6842105263 + 0.06925207760 = 0.7534626039 0.06925207760 + 0.5263157895z3 + z6 = 0.7534626039 Factor a perfect square on the left side: (z3 + 0.2631578948)(z3 + 0.2631578948) = 0.7534626039 Calculate the square root of the right side: 0.868022237 Break this problem into two subproblems by setting (z3 + 0.2631578948) equal to 0.868022237 and -0.868022237.Subproblem 1
z3 + 0.2631578948 = 0.868022237 Simplifying z3 + 0.2631578948 = 0.868022237 Reorder the terms: 0.2631578948 + z3 = 0.868022237 Solving 0.2631578948 + z3 = 0.868022237 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.2631578948' to each side of the equation. 0.2631578948 + -0.2631578948 + z3 = 0.868022237 + -0.2631578948 Combine like terms: 0.2631578948 + -0.2631578948 = 0.0000000000 0.0000000000 + z3 = 0.868022237 + -0.2631578948 z3 = 0.868022237 + -0.2631578948 Combine like terms: 0.868022237 + -0.2631578948 = 0.6048643422 z3 = 0.6048643422 Simplifying z3 = 0.6048643422 Reorder the terms: -0.6048643422 + z3 = 0.6048643422 + -0.6048643422 Combine like terms: 0.6048643422 + -0.6048643422 = 0.0000000000 -0.6048643422 + z3 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
z3 + 0.2631578948 = -0.868022237 Simplifying z3 + 0.2631578948 = -0.868022237 Reorder the terms: 0.2631578948 + z3 = -0.868022237 Solving 0.2631578948 + z3 = -0.868022237 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.2631578948' to each side of the equation. 0.2631578948 + -0.2631578948 + z3 = -0.868022237 + -0.2631578948 Combine like terms: 0.2631578948 + -0.2631578948 = 0.0000000000 0.0000000000 + z3 = -0.868022237 + -0.2631578948 z3 = -0.868022237 + -0.2631578948 Combine like terms: -0.868022237 + -0.2631578948 = -1.1311801318 z3 = -1.1311801318 Simplifying z3 = -1.1311801318 Reorder the terms: 1.1311801318 + z3 = -1.1311801318 + 1.1311801318 Combine like terms: -1.1311801318 + 1.1311801318 = 0.0000000000 1.1311801318 + z3 = 0.0000000000 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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