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Simplifying w2 + 18w + -130 = 0 Reorder the terms: -130 + 18w + w2 = 0 Solving -130 + 18w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 18w + 130 + w2 = 0 + 130 Reorder the terms: -130 + 130 + 18w + w2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 18w + w2 = 0 + 130 18w + w2 = 0 + 130 Combine like terms: 0 + 130 = 130 18w + w2 = 130 The w term is 18w. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18w + 81 + w2 = 130 + 81 Reorder the terms: 81 + 18w + w2 = 130 + 81 Combine like terms: 130 + 81 = 211 81 + 18w + w2 = 211 Factor a perfect square on the left side: (w + 9)(w + 9) = 211 Calculate the square root of the right side: 14.525839046 Break this problem into two subproblems by setting (w + 9) equal to 14.525839046 and -14.525839046.Subproblem 1
w + 9 = 14.525839046 Simplifying w + 9 = 14.525839046 Reorder the terms: 9 + w = 14.525839046 Solving 9 + w = 14.525839046 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = 14.525839046 + -9 Combine like terms: 9 + -9 = 0 0 + w = 14.525839046 + -9 w = 14.525839046 + -9 Combine like terms: 14.525839046 + -9 = 5.525839046 w = 5.525839046 Simplifying w = 5.525839046Subproblem 2
w + 9 = -14.525839046 Simplifying w + 9 = -14.525839046 Reorder the terms: 9 + w = -14.525839046 Solving 9 + w = -14.525839046 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = -14.525839046 + -9 Combine like terms: 9 + -9 = 0 0 + w = -14.525839046 + -9 w = -14.525839046 + -9 Combine like terms: -14.525839046 + -9 = -23.525839046 w = -23.525839046 Simplifying w = -23.525839046Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.525839046, -23.525839046}
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