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Simplifying (2w2 + -7w4 + 7) * 3w5 = 0 Reorder the terms: (7 + 2w2 + -7w4) * 3w5 = 0 Reorder the terms for easier multiplication: 3w5(7 + 2w2 + -7w4) = 0 (7 * 3w5 + 2w2 * 3w5 + -7w4 * 3w5) = 0 (21w5 + 6w7 + -21w9) = 0 Solving 21w5 + 6w7 + -21w9 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3w5'. 3w5(7 + 2w2 + -7w4) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'w5' equal to zero and attempt to solve: Simplifying w5 = 0 Solving w5 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w5 = 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 '(7 + 2w2 + -7w4)' equal to zero and attempt to solve: Simplifying 7 + 2w2 + -7w4 = 0 Solving 7 + 2w2 + -7w4 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1 + -0.2857142857w2 + w4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.2857142857w2 + 1 + w4 = 0 + 1 Reorder the terms: -1 + 1 + -0.2857142857w2 + w4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.2857142857w2 + w4 = 0 + 1 -0.2857142857w2 + w4 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.2857142857w2 + w4 = 1 The w term is -0.2857142857w2. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857w2 + 0.02040816328 + w4 = 1 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857w2 + w4 = 1 + 0.02040816328 Combine like terms: 1 + 0.02040816328 = 1.02040816328 0.02040816328 + -0.2857142857w2 + w4 = 1.02040816328 Factor a perfect square on the left side: (w2 + -0.1428571429)(w2 + -0.1428571429) = 1.02040816328 Calculate the square root of the right side: 1.010152545 Break this problem into two subproblems by setting (w2 + -0.1428571429) equal to 1.010152545 and -1.010152545.Subproblem 1
w2 + -0.1428571429 = 1.010152545 Simplifying w2 + -0.1428571429 = 1.010152545 Reorder the terms: -0.1428571429 + w2 = 1.010152545 Solving -0.1428571429 + w2 = 1.010152545 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + w2 = 1.010152545 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + w2 = 1.010152545 + 0.1428571429 w2 = 1.010152545 + 0.1428571429 Combine like terms: 1.010152545 + 0.1428571429 = 1.1530096879 w2 = 1.1530096879 Simplifying w2 = 1.1530096879 Take the square root of each side: w = {-1.073782887, 1.073782887}Subproblem 2
w2 + -0.1428571429 = -1.010152545 Simplifying w2 + -0.1428571429 = -1.010152545 Reorder the terms: -0.1428571429 + w2 = -1.010152545 Solving -0.1428571429 + w2 = -1.010152545 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + w2 = -1.010152545 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + w2 = -1.010152545 + 0.1428571429 w2 = -1.010152545 + 0.1428571429 Combine like terms: -1.010152545 + 0.1428571429 = -0.8672954021 w2 = -0.8672954021 Simplifying w2 = -0.8672954021 Reorder the terms: 0.8672954021 + w2 = -0.8672954021 + 0.8672954021 Combine like terms: -0.8672954021 + 0.8672954021 = 0.0000000000 0.8672954021 + w2 = 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. The solution to this equation could not be determined.
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