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Simplifying 2w2 + 12w + -360 = 0 Reorder the terms: -360 + 12w + 2w2 = 0 Solving -360 + 12w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-180 + 6w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-180 + 6w + w2)' equal to zero and attempt to solve: Simplifying -180 + 6w + w2 = 0 Solving -180 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 6w + 180 + w2 = 0 + 180 Reorder the terms: -180 + 180 + 6w + w2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 6w + w2 = 0 + 180 6w + w2 = 0 + 180 Combine like terms: 0 + 180 = 180 6w + w2 = 180 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 180 + 9 Reorder the terms: 9 + 6w + w2 = 180 + 9 Combine like terms: 180 + 9 = 189 9 + 6w + w2 = 189 Factor a perfect square on the left side: (w + 3)(w + 3) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (w + 3) equal to 13.747727085 and -13.747727085.Subproblem 1
w + 3 = 13.747727085 Simplifying w + 3 = 13.747727085 Reorder the terms: 3 + w = 13.747727085 Solving 3 + w = 13.747727085 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 13.747727085 + -3 Combine like terms: 3 + -3 = 0 0 + w = 13.747727085 + -3 w = 13.747727085 + -3 Combine like terms: 13.747727085 + -3 = 10.747727085 w = 10.747727085 Simplifying w = 10.747727085Subproblem 2
w + 3 = -13.747727085 Simplifying w + 3 = -13.747727085 Reorder the terms: 3 + w = -13.747727085 Solving 3 + w = -13.747727085 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -13.747727085 + -3 Combine like terms: 3 + -3 = 0 0 + w = -13.747727085 + -3 w = -13.747727085 + -3 Combine like terms: -13.747727085 + -3 = -16.747727085 w = -16.747727085 Simplifying w = -16.747727085Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.747727085, -16.747727085}Solution
w = {10.747727085, -16.747727085}
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