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Simplifying 3w3 + -6w2 + -27w = 0 Reorder the terms: -27w + -6w2 + 3w3 = 0 Solving -27w + -6w2 + 3w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3w'. 3w(-9 + -2w + 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 '(-9 + -2w + w2)' equal to zero and attempt to solve: Simplifying -9 + -2w + w2 = 0 Solving -9 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -2w + 9 + w2 = 0 + 9 Reorder the terms: -9 + 9 + -2w + w2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2w + w2 = 0 + 9 -2w + w2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2w + w2 = 9 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 9 + 1 Reorder the terms: 1 + -2w + w2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + -2w + w2 = 10 Factor a perfect square on the left side: (w + -1)(w + -1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (w + -1) equal to 3.16227766 and -3.16227766.Subproblem 1
w + -1 = 3.16227766 Simplifying w + -1 = 3.16227766 Reorder the terms: -1 + w = 3.16227766 Solving -1 + w = 3.16227766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + w = 3.16227766 + 1 w = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 w = 4.16227766 Simplifying w = 4.16227766Subproblem 2
w + -1 = -3.16227766 Simplifying w + -1 = -3.16227766 Reorder the terms: -1 + w = -3.16227766 Solving -1 + w = -3.16227766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + w = -3.16227766 + 1 w = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 w = -2.16227766 Simplifying w = -2.16227766Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.16227766, -2.16227766}Solution
w = {0, 4.16227766, -2.16227766}
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