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Simplifying w2 + -12w + -546 = 0 Reorder the terms: -546 + -12w + w2 = 0 Solving -546 + -12w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '546' to each side of the equation. -546 + -12w + 546 + w2 = 0 + 546 Reorder the terms: -546 + 546 + -12w + w2 = 0 + 546 Combine like terms: -546 + 546 = 0 0 + -12w + w2 = 0 + 546 -12w + w2 = 0 + 546 Combine like terms: 0 + 546 = 546 -12w + w2 = 546 The w term is -12w. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12w + 36 + w2 = 546 + 36 Reorder the terms: 36 + -12w + w2 = 546 + 36 Combine like terms: 546 + 36 = 582 36 + -12w + w2 = 582 Factor a perfect square on the left side: (w + -6)(w + -6) = 582 Calculate the square root of the right side: 24.124676164 Break this problem into two subproblems by setting (w + -6) equal to 24.124676164 and -24.124676164.Subproblem 1
w + -6 = 24.124676164 Simplifying w + -6 = 24.124676164 Reorder the terms: -6 + w = 24.124676164 Solving -6 + w = 24.124676164 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = 24.124676164 + 6 Combine like terms: -6 + 6 = 0 0 + w = 24.124676164 + 6 w = 24.124676164 + 6 Combine like terms: 24.124676164 + 6 = 30.124676164 w = 30.124676164 Simplifying w = 30.124676164Subproblem 2
w + -6 = -24.124676164 Simplifying w + -6 = -24.124676164 Reorder the terms: -6 + w = -24.124676164 Solving -6 + w = -24.124676164 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = -24.124676164 + 6 Combine like terms: -6 + 6 = 0 0 + w = -24.124676164 + 6 w = -24.124676164 + 6 Combine like terms: -24.124676164 + 6 = -18.124676164 w = -18.124676164 Simplifying w = -18.124676164Solution
The solution to the problem is based on the solutions from the subproblems. w = {30.124676164, -18.124676164}
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