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Simplifying w2 + 49 = 2w2 + 18w + 37 Reorder the terms: 49 + w2 = 2w2 + 18w + 37 Reorder the terms: 49 + w2 = 37 + 18w + 2w2 Solving 49 + w2 = 37 + 18w + 2w2 Solving for variable 'w'. Reorder the terms: 49 + -37 + -18w + w2 + -2w2 = 37 + 18w + 2w2 + -37 + -18w + -2w2 Combine like terms: 49 + -37 = 12 12 + -18w + w2 + -2w2 = 37 + 18w + 2w2 + -37 + -18w + -2w2 Combine like terms: w2 + -2w2 = -1w2 12 + -18w + -1w2 = 37 + 18w + 2w2 + -37 + -18w + -2w2 Reorder the terms: 12 + -18w + -1w2 = 37 + -37 + 18w + -18w + 2w2 + -2w2 Combine like terms: 37 + -37 = 0 12 + -18w + -1w2 = 0 + 18w + -18w + 2w2 + -2w2 12 + -18w + -1w2 = 18w + -18w + 2w2 + -2w2 Combine like terms: 18w + -18w = 0 12 + -18w + -1w2 = 0 + 2w2 + -2w2 12 + -18w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 12 + -18w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 18w + w2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 18w + 12 + w2 = 0 + 12 Reorder the terms: -12 + 12 + 18w + w2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 18w + w2 = 0 + 12 18w + w2 = 0 + 12 Combine like terms: 0 + 12 = 12 18w + w2 = 12 The w term is 18w. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18w + 81 + w2 = 12 + 81 Reorder the terms: 81 + 18w + w2 = 12 + 81 Combine like terms: 12 + 81 = 93 81 + 18w + w2 = 93 Factor a perfect square on the left side: (w + 9)(w + 9) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (w + 9) equal to 9.643650761 and -9.643650761.Subproblem 1
w + 9 = 9.643650761 Simplifying w + 9 = 9.643650761 Reorder the terms: 9 + w = 9.643650761 Solving 9 + w = 9.643650761 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = 9.643650761 + -9 Combine like terms: 9 + -9 = 0 0 + w = 9.643650761 + -9 w = 9.643650761 + -9 Combine like terms: 9.643650761 + -9 = 0.643650761 w = 0.643650761 Simplifying w = 0.643650761Subproblem 2
w + 9 = -9.643650761 Simplifying w + 9 = -9.643650761 Reorder the terms: 9 + w = -9.643650761 Solving 9 + w = -9.643650761 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = -9.643650761 + -9 Combine like terms: 9 + -9 = 0 0 + w = -9.643650761 + -9 w = -9.643650761 + -9 Combine like terms: -9.643650761 + -9 = -18.643650761 w = -18.643650761 Simplifying w = -18.643650761Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.643650761, -18.643650761}
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