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Simplifying w(w + 3) = 58 Reorder the terms: w(3 + w) = 58 (3 * w + w * w) = 58 (3w + w2) = 58 Solving 3w + w2 = 58 Solving for variable 'w'. Reorder the terms: -58 + 3w + w2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + 3w + 58 + w2 = 0 + 58 Reorder the terms: -58 + 58 + 3w + w2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 3w + w2 = 0 + 58 3w + w2 = 0 + 58 Combine like terms: 0 + 58 = 58 3w + w2 = 58 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 58 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 58 + 2.25 Combine like terms: 58 + 2.25 = 60.25 2.25 + 3w + w2 = 60.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (w + 1.5) equal to 7.762087348 and -7.762087348.Subproblem 1
w + 1.5 = 7.762087348 Simplifying w + 1.5 = 7.762087348 Reorder the terms: 1.5 + w = 7.762087348 Solving 1.5 + w = 7.762087348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 7.762087348 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 7.762087348 + -1.5 w = 7.762087348 + -1.5 Combine like terms: 7.762087348 + -1.5 = 6.262087348 w = 6.262087348 Simplifying w = 6.262087348Subproblem 2
w + 1.5 = -7.762087348 Simplifying w + 1.5 = -7.762087348 Reorder the terms: 1.5 + w = -7.762087348 Solving 1.5 + w = -7.762087348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -7.762087348 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -7.762087348 + -1.5 w = -7.762087348 + -1.5 Combine like terms: -7.762087348 + -1.5 = -9.262087348 w = -9.262087348 Simplifying w = -9.262087348Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.262087348, -9.262087348}
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