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Simplifying 2w2 + 8w + -52 = 0 Reorder the terms: -52 + 8w + 2w2 = 0 Solving -52 + 8w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-26 + 4w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-26 + 4w + w2)' equal to zero and attempt to solve: Simplifying -26 + 4w + w2 = 0 Solving -26 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 4w + 26 + w2 = 0 + 26 Reorder the terms: -26 + 26 + 4w + w2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 4w + w2 = 0 + 26 4w + w2 = 0 + 26 Combine like terms: 0 + 26 = 26 4w + w2 = 26 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 26 + 4 Reorder the terms: 4 + 4w + w2 = 26 + 4 Combine like terms: 26 + 4 = 30 4 + 4w + w2 = 30 Factor a perfect square on the left side: (w + 2)(w + 2) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (w + 2) equal to 5.477225575 and -5.477225575.Subproblem 1
w + 2 = 5.477225575 Simplifying w + 2 = 5.477225575 Reorder the terms: 2 + w = 5.477225575 Solving 2 + w = 5.477225575 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 5.477225575 + -2 Combine like terms: 2 + -2 = 0 0 + w = 5.477225575 + -2 w = 5.477225575 + -2 Combine like terms: 5.477225575 + -2 = 3.477225575 w = 3.477225575 Simplifying w = 3.477225575Subproblem 2
w + 2 = -5.477225575 Simplifying w + 2 = -5.477225575 Reorder the terms: 2 + w = -5.477225575 Solving 2 + w = -5.477225575 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -5.477225575 + -2 Combine like terms: 2 + -2 = 0 0 + w = -5.477225575 + -2 w = -5.477225575 + -2 Combine like terms: -5.477225575 + -2 = -7.477225575 w = -7.477225575 Simplifying w = -7.477225575Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.477225575, -7.477225575}Solution
w = {3.477225575, -7.477225575}
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