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Simplifying 3w3 + 21w2 + 9w = 0 Reorder the terms: 9w + 21w2 + 3w3 = 0 Solving 9w + 21w2 + 3w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3w'. 3w(3 + 7w + w2) = 0 Ignore the factor 3.Subproblem 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 '(3 + 7w + w2)' equal to zero and attempt to solve: Simplifying 3 + 7w + w2 = 0 Solving 3 + 7w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 7w + -3 + w2 = 0 + -3 Reorder the terms: 3 + -3 + 7w + w2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7w + w2 = 0 + -3 7w + w2 = 0 + -3 Combine like terms: 0 + -3 = -3 7w + w2 = -3 The w term is 7w. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7w + 12.25 + w2 = -3 + 12.25 Reorder the terms: 12.25 + 7w + w2 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + 7w + w2 = 9.25 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (w + 3.5) equal to 3.041381265 and -3.041381265.Subproblem 1
w + 3.5 = 3.041381265 Simplifying w + 3.5 = 3.041381265 Reorder the terms: 3.5 + w = 3.041381265 Solving 3.5 + w = 3.041381265 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = 3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 3.041381265 + -3.5 w = 3.041381265 + -3.5 Combine like terms: 3.041381265 + -3.5 = -0.458618735 w = -0.458618735 Simplifying w = -0.458618735Subproblem 2
w + 3.5 = -3.041381265 Simplifying w + 3.5 = -3.041381265 Reorder the terms: 3.5 + w = -3.041381265 Solving 3.5 + w = -3.041381265 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = -3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -3.041381265 + -3.5 w = -3.041381265 + -3.5 Combine like terms: -3.041381265 + -3.5 = -6.541381265 w = -6.541381265 Simplifying w = -6.541381265Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.458618735, -6.541381265}Solution
w = {0, -0.458618735, -6.541381265}
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