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Simplifying w2 + -9w + -72 = 0 Reorder the terms: -72 + -9w + w2 = 0 Solving -72 + -9w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -9w + 72 + w2 = 0 + 72 Reorder the terms: -72 + 72 + -9w + w2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -9w + w2 = 0 + 72 -9w + w2 = 0 + 72 Combine like terms: 0 + 72 = 72 -9w + w2 = 72 The w term is -9w. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9w + 20.25 + w2 = 72 + 20.25 Reorder the terms: 20.25 + -9w + w2 = 72 + 20.25 Combine like terms: 72 + 20.25 = 92.25 20.25 + -9w + w2 = 92.25 Factor a perfect square on the left side: (w + -4.5)(w + -4.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (w + -4.5) equal to 9.604686356 and -9.604686356.Subproblem 1
w + -4.5 = 9.604686356 Simplifying w + -4.5 = 9.604686356 Reorder the terms: -4.5 + w = 9.604686356 Solving -4.5 + w = 9.604686356 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w = 9.604686356 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = 9.604686356 + 4.5 w = 9.604686356 + 4.5 Combine like terms: 9.604686356 + 4.5 = 14.104686356 w = 14.104686356 Simplifying w = 14.104686356Subproblem 2
w + -4.5 = -9.604686356 Simplifying w + -4.5 = -9.604686356 Reorder the terms: -4.5 + w = -9.604686356 Solving -4.5 + w = -9.604686356 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w = -9.604686356 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = -9.604686356 + 4.5 w = -9.604686356 + 4.5 Combine like terms: -9.604686356 + 4.5 = -5.104686356 w = -5.104686356 Simplifying w = -5.104686356Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.104686356, -5.104686356}
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