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Simplifying 2w + 4w2 + -5w3 = 0 Solving 2w + 4w2 + -5w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(2 + 4w + -5w2) = 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 '(2 + 4w + -5w2)' equal to zero and attempt to solve: Simplifying 2 + 4w + -5w2 = 0 Solving 2 + 4w + -5w2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + -0.8w + w2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.8w + 0.4 + w2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.8w + w2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.8w + w2 = 0 + 0.4 -0.8w + w2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.8w + w2 = 0.4 The w term is -0.8w. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8w + 0.16 + w2 = 0.4 + 0.16 Reorder the terms: 0.16 + -0.8w + w2 = 0.4 + 0.16 Combine like terms: 0.4 + 0.16 = 0.56 0.16 + -0.8w + w2 = 0.56 Factor a perfect square on the left side: (w + -0.4)(w + -0.4) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (w + -0.4) equal to 0.748331477 and -0.748331477.Subproblem 1
w + -0.4 = 0.748331477 Simplifying w + -0.4 = 0.748331477 Reorder the terms: -0.4 + w = 0.748331477 Solving -0.4 + w = 0.748331477 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + w = 0.748331477 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + w = 0.748331477 + 0.4 w = 0.748331477 + 0.4 Combine like terms: 0.748331477 + 0.4 = 1.148331477 w = 1.148331477 Simplifying w = 1.148331477Subproblem 2
w + -0.4 = -0.748331477 Simplifying w + -0.4 = -0.748331477 Reorder the terms: -0.4 + w = -0.748331477 Solving -0.4 + w = -0.748331477 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + w = -0.748331477 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + w = -0.748331477 + 0.4 w = -0.748331477 + 0.4 Combine like terms: -0.748331477 + 0.4 = -0.348331477 w = -0.348331477 Simplifying w = -0.348331477Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.148331477, -0.348331477}Solution
w = {0, 1.148331477, -0.348331477}
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