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Simplifying w2 + 18w = 77 Reorder the terms: 18w + w2 = 77 Solving 18w + w2 = 77 Solving for variable 'w'. Reorder the terms: -77 + 18w + w2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + 18w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 18w + 77 + w2 = 0 + 77 Reorder the terms: -77 + 77 + 18w + w2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 18w + w2 = 0 + 77 18w + w2 = 0 + 77 Combine like terms: 0 + 77 = 77 18w + w2 = 77 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 = 77 + 81 Reorder the terms: 81 + 18w + w2 = 77 + 81 Combine like terms: 77 + 81 = 158 81 + 18w + w2 = 158 Factor a perfect square on the left side: (w + 9)(w + 9) = 158 Calculate the square root of the right side: 12.56980509 Break this problem into two subproblems by setting (w + 9) equal to 12.56980509 and -12.56980509.Subproblem 1
w + 9 = 12.56980509 Simplifying w + 9 = 12.56980509 Reorder the terms: 9 + w = 12.56980509 Solving 9 + w = 12.56980509 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 = 12.56980509 + -9 Combine like terms: 9 + -9 = 0 0 + w = 12.56980509 + -9 w = 12.56980509 + -9 Combine like terms: 12.56980509 + -9 = 3.56980509 w = 3.56980509 Simplifying w = 3.56980509Subproblem 2
w + 9 = -12.56980509 Simplifying w + 9 = -12.56980509 Reorder the terms: 9 + w = -12.56980509 Solving 9 + w = -12.56980509 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 = -12.56980509 + -9 Combine like terms: 9 + -9 = 0 0 + w = -12.56980509 + -9 w = -12.56980509 + -9 Combine like terms: -12.56980509 + -9 = -21.56980509 w = -21.56980509 Simplifying w = -21.56980509Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.56980509, -21.56980509}
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