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Simplifying 2w3 + -8w2 + -14w = 0 Reorder the terms: -14w + -8w2 + 2w3 = 0 Solving -14w + -8w2 + 2w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w'. 2w(-7 + -4w + w2) = 0 Ignore the factor 2.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 '(-7 + -4w + w2)' equal to zero and attempt to solve: Simplifying -7 + -4w + w2 = 0 Solving -7 + -4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -4w + 7 + w2 = 0 + 7 Reorder the terms: -7 + 7 + -4w + w2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4w + w2 = 0 + 7 -4w + w2 = 0 + 7 Combine like terms: 0 + 7 = 7 -4w + w2 = 7 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 7 + 4 Reorder the terms: 4 + -4w + w2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + -4w + w2 = 11 Factor a perfect square on the left side: (w + -2)(w + -2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (w + -2) equal to 3.31662479 and -3.31662479.Subproblem 1
w + -2 = 3.31662479 Simplifying w + -2 = 3.31662479 Reorder the terms: -2 + w = 3.31662479 Solving -2 + w = 3.31662479 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + w = 3.31662479 + 2 w = 3.31662479 + 2 Combine like terms: 3.31662479 + 2 = 5.31662479 w = 5.31662479 Simplifying w = 5.31662479Subproblem 2
w + -2 = -3.31662479 Simplifying w + -2 = -3.31662479 Reorder the terms: -2 + w = -3.31662479 Solving -2 + w = -3.31662479 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + w = -3.31662479 + 2 w = -3.31662479 + 2 Combine like terms: -3.31662479 + 2 = -1.31662479 w = -1.31662479 Simplifying w = -1.31662479Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.31662479, -1.31662479}Solution
w = {0, 5.31662479, -1.31662479}
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