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Simplifying w2 = 72 + -9w Solving w2 = 72 + -9w Solving for variable 'w'. Reorder the terms: -72 + 9w + w2 = 72 + -9w + -72 + 9w Reorder the terms: -72 + 9w + w2 = 72 + -72 + -9w + 9w Combine like terms: 72 + -72 = 0 -72 + 9w + w2 = 0 + -9w + 9w -72 + 9w + w2 = -9w + 9w Combine like terms: -9w + 9w = 0 -72 + 9w + w2 = 0 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 = 5.104686356 w = 5.104686356 Simplifying w = 5.104686356Subproblem 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 = -14.104686356 w = -14.104686356 Simplifying w = -14.104686356Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.104686356, -14.104686356}
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