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Simplifying w2 + 24w + -92 = 0 Reorder the terms: -92 + 24w + w2 = 0 Solving -92 + 24w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 24w + 92 + w2 = 0 + 92 Reorder the terms: -92 + 92 + 24w + w2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 24w + w2 = 0 + 92 24w + w2 = 0 + 92 Combine like terms: 0 + 92 = 92 24w + w2 = 92 The w term is 24w. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24w + 144 + w2 = 92 + 144 Reorder the terms: 144 + 24w + w2 = 92 + 144 Combine like terms: 92 + 144 = 236 144 + 24w + w2 = 236 Factor a perfect square on the left side: (w + 12)(w + 12) = 236 Calculate the square root of the right side: 15.362291496 Break this problem into two subproblems by setting (w + 12) equal to 15.362291496 and -15.362291496.Subproblem 1
w + 12 = 15.362291496 Simplifying w + 12 = 15.362291496 Reorder the terms: 12 + w = 15.362291496 Solving 12 + w = 15.362291496 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + w = 15.362291496 + -12 Combine like terms: 12 + -12 = 0 0 + w = 15.362291496 + -12 w = 15.362291496 + -12 Combine like terms: 15.362291496 + -12 = 3.362291496 w = 3.362291496 Simplifying w = 3.362291496Subproblem 2
w + 12 = -15.362291496 Simplifying w + 12 = -15.362291496 Reorder the terms: 12 + w = -15.362291496 Solving 12 + w = -15.362291496 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + w = -15.362291496 + -12 Combine like terms: 12 + -12 = 0 0 + w = -15.362291496 + -12 w = -15.362291496 + -12 Combine like terms: -15.362291496 + -12 = -27.362291496 w = -27.362291496 Simplifying w = -27.362291496Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.362291496, -27.362291496}
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