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Simplifying 86 + -27w + w2 = 0 Solving 86 + -27w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-86' to each side of the equation. 86 + -27w + -86 + w2 = 0 + -86 Reorder the terms: 86 + -86 + -27w + w2 = 0 + -86 Combine like terms: 86 + -86 = 0 0 + -27w + w2 = 0 + -86 -27w + w2 = 0 + -86 Combine like terms: 0 + -86 = -86 -27w + w2 = -86 The w term is -27w. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27w + 182.25 + w2 = -86 + 182.25 Reorder the terms: 182.25 + -27w + w2 = -86 + 182.25 Combine like terms: -86 + 182.25 = 96.25 182.25 + -27w + w2 = 96.25 Factor a perfect square on the left side: (w + -13.5)(w + -13.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (w + -13.5) equal to 9.810708435 and -9.810708435.Subproblem 1
w + -13.5 = 9.810708435 Simplifying w + -13.5 = 9.810708435 Reorder the terms: -13.5 + w = 9.810708435 Solving -13.5 + w = 9.810708435 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + w = 9.810708435 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + w = 9.810708435 + 13.5 w = 9.810708435 + 13.5 Combine like terms: 9.810708435 + 13.5 = 23.310708435 w = 23.310708435 Simplifying w = 23.310708435Subproblem 2
w + -13.5 = -9.810708435 Simplifying w + -13.5 = -9.810708435 Reorder the terms: -13.5 + w = -9.810708435 Solving -13.5 + w = -9.810708435 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + w = -9.810708435 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + w = -9.810708435 + 13.5 w = -9.810708435 + 13.5 Combine like terms: -9.810708435 + 13.5 = 3.689291565 w = 3.689291565 Simplifying w = 3.689291565Solution
The solution to the problem is based on the solutions from the subproblems. w = {23.310708435, 3.689291565}
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