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Simplifying 63 = w2 + 9w Reorder the terms: 63 = 9w + w2 Solving 63 = 9w + w2 Solving for variable 'w'. Reorder the terms: 63 + -9w + -1w2 = 9w + -9w + w2 + -1w2 Combine like terms: 9w + -9w = 0 63 + -9w + -1w2 = 0 + w2 + -1w2 63 + -9w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 63 + -9w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + 9w + w2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 9w + 63 + w2 = 0 + 63 Reorder the terms: -63 + 63 + 9w + w2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 9w + w2 = 0 + 63 9w + w2 = 0 + 63 Combine like terms: 0 + 63 = 63 9w + w2 = 63 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 = 63 + 20.25 Reorder the terms: 20.25 + 9w + w2 = 63 + 20.25 Combine like terms: 63 + 20.25 = 83.25 20.25 + 9w + w2 = 83.25 Factor a perfect square on the left side: (w + 4.5)(w + 4.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (w + 4.5) equal to 9.124143795 and -9.124143795.Subproblem 1
w + 4.5 = 9.124143795 Simplifying w + 4.5 = 9.124143795 Reorder the terms: 4.5 + w = 9.124143795 Solving 4.5 + w = 9.124143795 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 = 9.124143795 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = 9.124143795 + -4.5 w = 9.124143795 + -4.5 Combine like terms: 9.124143795 + -4.5 = 4.624143795 w = 4.624143795 Simplifying w = 4.624143795Subproblem 2
w + 4.5 = -9.124143795 Simplifying w + 4.5 = -9.124143795 Reorder the terms: 4.5 + w = -9.124143795 Solving 4.5 + w = -9.124143795 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 = -9.124143795 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = -9.124143795 + -4.5 w = -9.124143795 + -4.5 Combine like terms: -9.124143795 + -4.5 = -13.624143795 w = -13.624143795 Simplifying w = -13.624143795Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.624143795, -13.624143795}
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