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Simplifying w2 + -55w + 100 = 0 Reorder the terms: 100 + -55w + w2 = 0 Solving 100 + -55w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -55w + -100 + w2 = 0 + -100 Reorder the terms: 100 + -100 + -55w + w2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -55w + w2 = 0 + -100 -55w + w2 = 0 + -100 Combine like terms: 0 + -100 = -100 -55w + w2 = -100 The w term is -55w. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55w + 756.25 + w2 = -100 + 756.25 Reorder the terms: 756.25 + -55w + w2 = -100 + 756.25 Combine like terms: -100 + 756.25 = 656.25 756.25 + -55w + w2 = 656.25 Factor a perfect square on the left side: (w + -27.5)(w + -27.5) = 656.25 Calculate the square root of the right side: 25.617376915 Break this problem into two subproblems by setting (w + -27.5) equal to 25.617376915 and -25.617376915.Subproblem 1
w + -27.5 = 25.617376915 Simplifying w + -27.5 = 25.617376915 Reorder the terms: -27.5 + w = 25.617376915 Solving -27.5 + w = 25.617376915 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + w = 25.617376915 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + w = 25.617376915 + 27.5 w = 25.617376915 + 27.5 Combine like terms: 25.617376915 + 27.5 = 53.117376915 w = 53.117376915 Simplifying w = 53.117376915Subproblem 2
w + -27.5 = -25.617376915 Simplifying w + -27.5 = -25.617376915 Reorder the terms: -27.5 + w = -25.617376915 Solving -27.5 + w = -25.617376915 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + w = -25.617376915 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + w = -25.617376915 + 27.5 w = -25.617376915 + 27.5 Combine like terms: -25.617376915 + 27.5 = 1.882623085 w = 1.882623085 Simplifying w = 1.882623085Solution
The solution to the problem is based on the solutions from the subproblems. w = {53.117376915, 1.882623085}
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