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Simplifying w2 + 5w + -72 = 0 Reorder the terms: -72 + 5w + w2 = 0 Solving -72 + 5w + 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 + 5w + 72 + w2 = 0 + 72 Reorder the terms: -72 + 72 + 5w + w2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 5w + w2 = 0 + 72 5w + w2 = 0 + 72 Combine like terms: 0 + 72 = 72 5w + w2 = 72 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = 72 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 72 + 6.25 Combine like terms: 72 + 6.25 = 78.25 6.25 + 5w + w2 = 78.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (w + 2.5) equal to 8.845903006 and -8.845903006.Subproblem 1
w + 2.5 = 8.845903006 Simplifying w + 2.5 = 8.845903006 Reorder the terms: 2.5 + w = 8.845903006 Solving 2.5 + w = 8.845903006 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 8.845903006 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 8.845903006 + -2.5 w = 8.845903006 + -2.5 Combine like terms: 8.845903006 + -2.5 = 6.345903006 w = 6.345903006 Simplifying w = 6.345903006Subproblem 2
w + 2.5 = -8.845903006 Simplifying w + 2.5 = -8.845903006 Reorder the terms: 2.5 + w = -8.845903006 Solving 2.5 + w = -8.845903006 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -8.845903006 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -8.845903006 + -2.5 w = -8.845903006 + -2.5 Combine like terms: -8.845903006 + -2.5 = -11.345903006 w = -11.345903006 Simplifying w = -11.345903006Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.345903006, -11.345903006}
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