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Simplifying 2w2 + -4w = 28 Reorder the terms: -4w + 2w2 = 28 Solving -4w + 2w2 = 28 Solving for variable 'w'. Reorder the terms: -28 + -4w + 2w2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -4w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -2w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -2w + w2)' equal to zero and attempt to solve: Simplifying -14 + -2w + w2 = 0 Solving -14 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -2w + 14 + w2 = 0 + 14 Reorder the terms: -14 + 14 + -2w + w2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -2w + w2 = 0 + 14 -2w + w2 = 0 + 14 Combine like terms: 0 + 14 = 14 -2w + w2 = 14 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 14 + 1 Reorder the terms: 1 + -2w + w2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + -2w + w2 = 15 Factor a perfect square on the left side: (w + -1)(w + -1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (w + -1) equal to 3.872983346 and -3.872983346.Subproblem 1
w + -1 = 3.872983346 Simplifying w + -1 = 3.872983346 Reorder the terms: -1 + w = 3.872983346 Solving -1 + w = 3.872983346 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + w = 3.872983346 + 1 w = 3.872983346 + 1 Combine like terms: 3.872983346 + 1 = 4.872983346 w = 4.872983346 Simplifying w = 4.872983346Subproblem 2
w + -1 = -3.872983346 Simplifying w + -1 = -3.872983346 Reorder the terms: -1 + w = -3.872983346 Solving -1 + w = -3.872983346 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + w = -3.872983346 + 1 w = -3.872983346 + 1 Combine like terms: -3.872983346 + 1 = -2.872983346 w = -2.872983346 Simplifying w = -2.872983346Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.872983346, -2.872983346}Solution
w = {4.872983346, -2.872983346}
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