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Simplifying w2 + 15w = 99 Reorder the terms: 15w + w2 = 99 Solving 15w + w2 = 99 Solving for variable 'w'. Reorder the terms: -99 + 15w + w2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 15w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 15w + 99 + w2 = 0 + 99 Reorder the terms: -99 + 99 + 15w + w2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 15w + w2 = 0 + 99 15w + w2 = 0 + 99 Combine like terms: 0 + 99 = 99 15w + w2 = 99 The w term is 15w. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15w + 56.25 + w2 = 99 + 56.25 Reorder the terms: 56.25 + 15w + w2 = 99 + 56.25 Combine like terms: 99 + 56.25 = 155.25 56.25 + 15w + w2 = 155.25 Factor a perfect square on the left side: (w + 7.5)(w + 7.5) = 155.25 Calculate the square root of the right side: 12.459935794 Break this problem into two subproblems by setting (w + 7.5) equal to 12.459935794 and -12.459935794.Subproblem 1
w + 7.5 = 12.459935794 Simplifying w + 7.5 = 12.459935794 Reorder the terms: 7.5 + w = 12.459935794 Solving 7.5 + w = 12.459935794 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = 12.459935794 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 12.459935794 + -7.5 w = 12.459935794 + -7.5 Combine like terms: 12.459935794 + -7.5 = 4.959935794 w = 4.959935794 Simplifying w = 4.959935794Subproblem 2
w + 7.5 = -12.459935794 Simplifying w + 7.5 = -12.459935794 Reorder the terms: 7.5 + w = -12.459935794 Solving 7.5 + w = -12.459935794 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = -12.459935794 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -12.459935794 + -7.5 w = -12.459935794 + -7.5 Combine like terms: -12.459935794 + -7.5 = -19.959935794 w = -19.959935794 Simplifying w = -19.959935794Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.959935794, -19.959935794}
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