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Simplifying w2 + -7w + -110 = 0 Reorder the terms: -110 + -7w + w2 = 0 Solving -110 + -7w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + -7w + 110 + w2 = 0 + 110 Reorder the terms: -110 + 110 + -7w + w2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -7w + w2 = 0 + 110 -7w + w2 = 0 + 110 Combine like terms: 0 + 110 = 110 -7w + w2 = 110 The w term is -7w. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7w + 12.25 + w2 = 110 + 12.25 Reorder the terms: 12.25 + -7w + w2 = 110 + 12.25 Combine like terms: 110 + 12.25 = 122.25 12.25 + -7w + w2 = 122.25 Factor a perfect square on the left side: (w + -3.5)(w + -3.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (w + -3.5) equal to 11.056672194 and -11.056672194.Subproblem 1
w + -3.5 = 11.056672194 Simplifying w + -3.5 = 11.056672194 Reorder the terms: -3.5 + w = 11.056672194 Solving -3.5 + w = 11.056672194 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + w = 11.056672194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = 11.056672194 + 3.5 w = 11.056672194 + 3.5 Combine like terms: 11.056672194 + 3.5 = 14.556672194 w = 14.556672194 Simplifying w = 14.556672194Subproblem 2
w + -3.5 = -11.056672194 Simplifying w + -3.5 = -11.056672194 Reorder the terms: -3.5 + w = -11.056672194 Solving -3.5 + w = -11.056672194 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + w = -11.056672194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + w = -11.056672194 + 3.5 w = -11.056672194 + 3.5 Combine like terms: -11.056672194 + 3.5 = -7.556672194 w = -7.556672194 Simplifying w = -7.556672194Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.556672194, -7.556672194}
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