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Simplifying 2(17w2 + 30w + -1360) = 0 Reorder the terms: 2(-1360 + 30w + 17w2) = 0 (-1360 * 2 + 30w * 2 + 17w2 * 2) = 0 (-2720 + 60w + 34w2) = 0 Solving -2720 + 60w + 34w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1360 + 30w + 17w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1360 + 30w + 17w2)' equal to zero and attempt to solve: Simplifying -1360 + 30w + 17w2 = 0 Solving -1360 + 30w + 17w2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -80 + 1.764705882w + w2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 1.764705882w + 80 + w2 = 0 + 80 Reorder the terms: -80 + 80 + 1.764705882w + w2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 1.764705882w + w2 = 0 + 80 1.764705882w + w2 = 0 + 80 Combine like terms: 0 + 80 = 80 1.764705882w + w2 = 80 The w term is 1.764705882w. Take half its coefficient (0.882352941). Square it (0.7785467125) and add it to both sides. Add '0.7785467125' to each side of the equation. 1.764705882w + 0.7785467125 + w2 = 80 + 0.7785467125 Reorder the terms: 0.7785467125 + 1.764705882w + w2 = 80 + 0.7785467125 Combine like terms: 80 + 0.7785467125 = 80.7785467125 0.7785467125 + 1.764705882w + w2 = 80.7785467125 Factor a perfect square on the left side: (w + 0.882352941)(w + 0.882352941) = 80.7785467125 Calculate the square root of the right side: 8.987688619 Break this problem into two subproblems by setting (w + 0.882352941) equal to 8.987688619 and -8.987688619.Subproblem 1
w + 0.882352941 = 8.987688619 Simplifying w + 0.882352941 = 8.987688619 Reorder the terms: 0.882352941 + w = 8.987688619 Solving 0.882352941 + w = 8.987688619 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.882352941' to each side of the equation. 0.882352941 + -0.882352941 + w = 8.987688619 + -0.882352941 Combine like terms: 0.882352941 + -0.882352941 = 0.000000000 0.000000000 + w = 8.987688619 + -0.882352941 w = 8.987688619 + -0.882352941 Combine like terms: 8.987688619 + -0.882352941 = 8.105335678 w = 8.105335678 Simplifying w = 8.105335678Subproblem 2
w + 0.882352941 = -8.987688619 Simplifying w + 0.882352941 = -8.987688619 Reorder the terms: 0.882352941 + w = -8.987688619 Solving 0.882352941 + w = -8.987688619 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.882352941' to each side of the equation. 0.882352941 + -0.882352941 + w = -8.987688619 + -0.882352941 Combine like terms: 0.882352941 + -0.882352941 = 0.000000000 0.000000000 + w = -8.987688619 + -0.882352941 w = -8.987688619 + -0.882352941 Combine like terms: -8.987688619 + -0.882352941 = -9.87004156 w = -9.87004156 Simplifying w = -9.87004156Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.105335678, -9.87004156}Solution
w = {8.105335678, -9.87004156}
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