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Simplifying w2 + 4w + -3600 = 0 Reorder the terms: -3600 + 4w + w2 = 0 Solving -3600 + 4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 4w + 3600 + w2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 4w + w2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 4w + w2 = 0 + 3600 4w + w2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 4w + w2 = 3600 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 3600 + 4 Reorder the terms: 4 + 4w + w2 = 3600 + 4 Combine like terms: 3600 + 4 = 3604 4 + 4w + w2 = 3604 Factor a perfect square on the left side: (w + 2)(w + 2) = 3604 Calculate the square root of the right side: 60.033324079 Break this problem into two subproblems by setting (w + 2) equal to 60.033324079 and -60.033324079.Subproblem 1
w + 2 = 60.033324079 Simplifying w + 2 = 60.033324079 Reorder the terms: 2 + w = 60.033324079 Solving 2 + w = 60.033324079 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 60.033324079 + -2 Combine like terms: 2 + -2 = 0 0 + w = 60.033324079 + -2 w = 60.033324079 + -2 Combine like terms: 60.033324079 + -2 = 58.033324079 w = 58.033324079 Simplifying w = 58.033324079Subproblem 2
w + 2 = -60.033324079 Simplifying w + 2 = -60.033324079 Reorder the terms: 2 + w = -60.033324079 Solving 2 + w = -60.033324079 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -60.033324079 + -2 Combine like terms: 2 + -2 = 0 0 + w = -60.033324079 + -2 w = -60.033324079 + -2 Combine like terms: -60.033324079 + -2 = -62.033324079 w = -62.033324079 Simplifying w = -62.033324079Solution
The solution to the problem is based on the solutions from the subproblems. w = {58.033324079, -62.033324079}
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