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Simplifying w2 + 16w + 48 = 320 Reorder the terms: 48 + 16w + w2 = 320 Solving 48 + 16w + w2 = 320 Solving for variable 'w'. Reorder the terms: 48 + -320 + 16w + w2 = 320 + -320 Combine like terms: 48 + -320 = -272 -272 + 16w + w2 = 320 + -320 Combine like terms: 320 + -320 = 0 -272 + 16w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '272' to each side of the equation. -272 + 16w + 272 + w2 = 0 + 272 Reorder the terms: -272 + 272 + 16w + w2 = 0 + 272 Combine like terms: -272 + 272 = 0 0 + 16w + w2 = 0 + 272 16w + w2 = 0 + 272 Combine like terms: 0 + 272 = 272 16w + w2 = 272 The w term is 16w. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16w + 64 + w2 = 272 + 64 Reorder the terms: 64 + 16w + w2 = 272 + 64 Combine like terms: 272 + 64 = 336 64 + 16w + w2 = 336 Factor a perfect square on the left side: (w + 8)(w + 8) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (w + 8) equal to 18.33030278 and -18.33030278.Subproblem 1
w + 8 = 18.33030278 Simplifying w + 8 = 18.33030278 Reorder the terms: 8 + w = 18.33030278 Solving 8 + w = 18.33030278 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = 18.33030278 + -8 Combine like terms: 8 + -8 = 0 0 + w = 18.33030278 + -8 w = 18.33030278 + -8 Combine like terms: 18.33030278 + -8 = 10.33030278 w = 10.33030278 Simplifying w = 10.33030278Subproblem 2
w + 8 = -18.33030278 Simplifying w + 8 = -18.33030278 Reorder the terms: 8 + w = -18.33030278 Solving 8 + w = -18.33030278 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = -18.33030278 + -8 Combine like terms: 8 + -8 = 0 0 + w = -18.33030278 + -8 w = -18.33030278 + -8 Combine like terms: -18.33030278 + -8 = -26.33030278 w = -26.33030278 Simplifying w = -26.33030278Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.33030278, -26.33030278}
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