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Simplifying 8w3 + -2w7 + 2w5 + w5 + 5w3 = 0 Reorder the terms: 8w3 + 5w3 + 2w5 + w5 + -2w7 = 0 Combine like terms: 8w3 + 5w3 = 13w3 13w3 + 2w5 + w5 + -2w7 = 0 Combine like terms: 2w5 + w5 = 3w5 13w3 + 3w5 + -2w7 = 0 Solving 13w3 + 3w5 + -2w7 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w3'. w3(13 + 3w2 + -2w4) = 0Subproblem 1
Set the factor 'w3' equal to zero and attempt to solve: Simplifying w3 = 0 Solving w3 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(13 + 3w2 + -2w4)' equal to zero and attempt to solve: Simplifying 13 + 3w2 + -2w4 = 0 Solving 13 + 3w2 + -2w4 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6.5 + -1.5w2 + w4 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -1.5w2 + 6.5 + w4 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -1.5w2 + w4 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -1.5w2 + w4 = 0 + 6.5 -1.5w2 + w4 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -1.5w2 + w4 = 6.5 The w term is -1.5w2. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5w2 + 0.5625 + w4 = 6.5 + 0.5625 Reorder the terms: 0.5625 + -1.5w2 + w4 = 6.5 + 0.5625 Combine like terms: 6.5 + 0.5625 = 7.0625 0.5625 + -1.5w2 + w4 = 7.0625 Factor a perfect square on the left side: (w2 + -0.75)(w2 + -0.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (w2 + -0.75) equal to 2.657536453 and -2.657536453.Subproblem 1
w2 + -0.75 = 2.657536453 Simplifying w2 + -0.75 = 2.657536453 Reorder the terms: -0.75 + w2 = 2.657536453 Solving -0.75 + w2 = 2.657536453 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w2 = 2.657536453 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w2 = 2.657536453 + 0.75 w2 = 2.657536453 + 0.75 Combine like terms: 2.657536453 + 0.75 = 3.407536453 w2 = 3.407536453 Simplifying w2 = 3.407536453 Take the square root of each side: w = {-1.845951368, 1.845951368}Subproblem 2
w2 + -0.75 = -2.657536453 Simplifying w2 + -0.75 = -2.657536453 Reorder the terms: -0.75 + w2 = -2.657536453 Solving -0.75 + w2 = -2.657536453 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w2 = -2.657536453 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w2 = -2.657536453 + 0.75 w2 = -2.657536453 + 0.75 Combine like terms: -2.657536453 + 0.75 = -1.907536453 w2 = -1.907536453 Simplifying w2 = -1.907536453 Reorder the terms: 1.907536453 + w2 = -1.907536453 + 1.907536453 Combine like terms: -1.907536453 + 1.907536453 = 0.000000000 1.907536453 + w2 = 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. The solution to this equation could not be determined.
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