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Simplifying w2 + 8w + 128 = 230 Reorder the terms: 128 + 8w + w2 = 230 Solving 128 + 8w + w2 = 230 Solving for variable 'w'. Reorder the terms: 128 + -230 + 8w + w2 = 230 + -230 Combine like terms: 128 + -230 = -102 -102 + 8w + w2 = 230 + -230 Combine like terms: 230 + -230 = 0 -102 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + 8w + 102 + w2 = 0 + 102 Reorder the terms: -102 + 102 + 8w + w2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 8w + w2 = 0 + 102 8w + w2 = 0 + 102 Combine like terms: 0 + 102 = 102 8w + w2 = 102 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = 102 + 16 Reorder the terms: 16 + 8w + w2 = 102 + 16 Combine like terms: 102 + 16 = 118 16 + 8w + w2 = 118 Factor a perfect square on the left side: (w + 4)(w + 4) = 118 Calculate the square root of the right side: 10.862780491 Break this problem into two subproblems by setting (w + 4) equal to 10.862780491 and -10.862780491.Subproblem 1
w + 4 = 10.862780491 Simplifying w + 4 = 10.862780491 Reorder the terms: 4 + w = 10.862780491 Solving 4 + w = 10.862780491 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 10.862780491 + -4 Combine like terms: 4 + -4 = 0 0 + w = 10.862780491 + -4 w = 10.862780491 + -4 Combine like terms: 10.862780491 + -4 = 6.862780491 w = 6.862780491 Simplifying w = 6.862780491Subproblem 2
w + 4 = -10.862780491 Simplifying w + 4 = -10.862780491 Reorder the terms: 4 + w = -10.862780491 Solving 4 + w = -10.862780491 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -10.862780491 + -4 Combine like terms: 4 + -4 = 0 0 + w = -10.862780491 + -4 w = -10.862780491 + -4 Combine like terms: -10.862780491 + -4 = -14.862780491 w = -14.862780491 Simplifying w = -14.862780491Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.862780491, -14.862780491}
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