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Simplifying 190 = w2 + -1w Reorder the terms: 190 = -1w + w2 Solving 190 = -1w + w2 Solving for variable 'w'. Reorder the terms: 190 + w + -1w2 = -1w + w + w2 + -1w2 Combine like terms: -1w + w = 0 190 + w + -1w2 = 0 + w2 + -1w2 190 + w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 190 + w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -190 + -1w + w2 = 0 Move the constant term to the right: Add '190' to each side of the equation. -190 + -1w + 190 + w2 = 0 + 190 Reorder the terms: -190 + 190 + -1w + w2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + -1w + w2 = 0 + 190 -1w + w2 = 0 + 190 Combine like terms: 0 + 190 = 190 -1w + w2 = 190 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1w + 0.25 + w2 = 190 + 0.25 Reorder the terms: 0.25 + -1w + w2 = 190 + 0.25 Combine like terms: 190 + 0.25 = 190.25 0.25 + -1w + w2 = 190.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (w + 0.5) equal to 13.793114224 and -13.793114224.Subproblem 1
w + 0.5 = 13.793114224 Simplifying w + 0.5 = 13.793114224 Reorder the terms: 0.5 + w = 13.793114224 Solving 0.5 + w = 13.793114224 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 13.793114224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 13.793114224 + -0.5 w = 13.793114224 + -0.5 Combine like terms: 13.793114224 + -0.5 = 13.293114224 w = 13.293114224 Simplifying w = 13.293114224Subproblem 2
w + 0.5 = -13.793114224 Simplifying w + 0.5 = -13.793114224 Reorder the terms: 0.5 + w = -13.793114224 Solving 0.5 + w = -13.793114224 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -13.793114224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -13.793114224 + -0.5 w = -13.793114224 + -0.5 Combine like terms: -13.793114224 + -0.5 = -14.293114224 w = -14.293114224 Simplifying w = -14.293114224Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.293114224, -14.293114224}
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