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Simplifying 2w2 + -6w + -180 = 0 Reorder the terms: -180 + -6w + 2w2 = 0 Solving -180 + -6w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + -3w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + -3w + w2)' equal to zero and attempt to solve: Simplifying -90 + -3w + w2 = 0 Solving -90 + -3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -3w + 90 + w2 = 0 + 90 Reorder the terms: -90 + 90 + -3w + w2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -3w + w2 = 0 + 90 -3w + w2 = 0 + 90 Combine like terms: 0 + 90 = 90 -3w + w2 = 90 The w term is -3w. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3w + 2.25 + w2 = 90 + 2.25 Reorder the terms: 2.25 + -3w + w2 = 90 + 2.25 Combine like terms: 90 + 2.25 = 92.25 2.25 + -3w + w2 = 92.25 Factor a perfect square on the left side: (w + -1.5)(w + -1.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (w + -1.5) equal to 9.604686356 and -9.604686356.Subproblem 1
w + -1.5 = 9.604686356 Simplifying w + -1.5 = 9.604686356 Reorder the terms: -1.5 + w = 9.604686356 Solving -1.5 + w = 9.604686356 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = 9.604686356 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = 9.604686356 + 1.5 w = 9.604686356 + 1.5 Combine like terms: 9.604686356 + 1.5 = 11.104686356 w = 11.104686356 Simplifying w = 11.104686356Subproblem 2
w + -1.5 = -9.604686356 Simplifying w + -1.5 = -9.604686356 Reorder the terms: -1.5 + w = -9.604686356 Solving -1.5 + w = -9.604686356 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = -9.604686356 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = -9.604686356 + 1.5 w = -9.604686356 + 1.5 Combine like terms: -9.604686356 + 1.5 = -8.104686356 w = -8.104686356 Simplifying w = -8.104686356Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.104686356, -8.104686356}Solution
w = {11.104686356, -8.104686356}
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