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Simplifying 8w7 + -1w4 + -1w = 0 Reorder the terms: -1w + -1w4 + 8w7 = 0 Solving -1w + -1w4 + 8w7 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(-1 + -1w3 + 8w6) = 0Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(-1 + -1w3 + 8w6)' equal to zero and attempt to solve: Simplifying -1 + -1w3 + 8w6 = 0 Solving -1 + -1w3 + 8w6 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.125w3 + w6 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.125w3 + 0.125 + w6 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.125w3 + w6 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.125w3 + w6 = 0 + 0.125 -0.125w3 + w6 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.125w3 + w6 = 0.125 The w term is -0.125w3. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125w3 + 0.00390625 + w6 = 0.125 + 0.00390625 Reorder the terms: 0.00390625 + -0.125w3 + w6 = 0.125 + 0.00390625 Combine like terms: 0.125 + 0.00390625 = 0.12890625 0.00390625 + -0.125w3 + w6 = 0.12890625 Factor a perfect square on the left side: (w3 + -0.0625)(w3 + -0.0625) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (w3 + -0.0625) equal to 0.359035165 and -0.359035165.Subproblem 1
w3 + -0.0625 = 0.359035165 Simplifying w3 + -0.0625 = 0.359035165 Reorder the terms: -0.0625 + w3 = 0.359035165 Solving -0.0625 + w3 = 0.359035165 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + w3 = 0.359035165 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + w3 = 0.359035165 + 0.0625 w3 = 0.359035165 + 0.0625 Combine like terms: 0.359035165 + 0.0625 = 0.421535165 w3 = 0.421535165 Simplifying w3 = 0.421535165 Reorder the terms: -0.421535165 + w3 = 0.421535165 + -0.421535165 Combine like terms: 0.421535165 + -0.421535165 = 0.000000000 -0.421535165 + w3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
w3 + -0.0625 = -0.359035165 Simplifying w3 + -0.0625 = -0.359035165 Reorder the terms: -0.0625 + w3 = -0.359035165 Solving -0.0625 + w3 = -0.359035165 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + w3 = -0.359035165 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + w3 = -0.359035165 + 0.0625 w3 = -0.359035165 + 0.0625 Combine like terms: -0.359035165 + 0.0625 = -0.296535165 w3 = -0.296535165 Simplifying w3 = -0.296535165 Reorder the terms: 0.296535165 + w3 = -0.296535165 + 0.296535165 Combine like terms: -0.296535165 + 0.296535165 = 0.000000000 0.296535165 + w3 = 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
w = {0}
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