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Simplifying 2w2 + 4w + -20 = 0 Reorder the terms: -20 + 4w + 2w2 = 0 Solving -20 + 4w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 2w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 2w + w2)' equal to zero and attempt to solve: Simplifying -10 + 2w + w2 = 0 Solving -10 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 2w + 10 + w2 = 0 + 10 Reorder the terms: -10 + 10 + 2w + w2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2w + w2 = 0 + 10 2w + w2 = 0 + 10 Combine like terms: 0 + 10 = 10 2w + w2 = 10 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 = 10 + 1 Reorder the terms: 1 + 2w + w2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2w + w2 = 11 Factor a perfect square on the left side: (w + 1)(w + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (w + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
w + 1 = 3.31662479 Simplifying w + 1 = 3.31662479 Reorder the terms: 1 + w = 3.31662479 Solving 1 + w = 3.31662479 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 = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + w = 3.31662479 + -1 w = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 w = 2.31662479 Simplifying w = 2.31662479Subproblem 2
w + 1 = -3.31662479 Simplifying w + 1 = -3.31662479 Reorder the terms: 1 + w = -3.31662479 Solving 1 + w = -3.31662479 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 = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + w = -3.31662479 + -1 w = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 w = -4.31662479 Simplifying w = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.31662479, -4.31662479}Solution
w = {2.31662479, -4.31662479}
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