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Simplifying 2w2 + -4w + -190 = 0 Reorder the terms: -190 + -4w + 2w2 = 0 Solving -190 + -4w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-95 + -2w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-95 + -2w + w2)' equal to zero and attempt to solve: Simplifying -95 + -2w + w2 = 0 Solving -95 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + -2w + 95 + w2 = 0 + 95 Reorder the terms: -95 + 95 + -2w + w2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + -2w + w2 = 0 + 95 -2w + w2 = 0 + 95 Combine like terms: 0 + 95 = 95 -2w + w2 = 95 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 = 95 + 1 Reorder the terms: 1 + -2w + w2 = 95 + 1 Combine like terms: 95 + 1 = 96 1 + -2w + w2 = 96 Factor a perfect square on the left side: (w + -1)(w + -1) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (w + -1) equal to 9.797958971 and -9.797958971.Subproblem 1
w + -1 = 9.797958971 Simplifying w + -1 = 9.797958971 Reorder the terms: -1 + w = 9.797958971 Solving -1 + w = 9.797958971 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 = 9.797958971 + 1 Combine like terms: -1 + 1 = 0 0 + w = 9.797958971 + 1 w = 9.797958971 + 1 Combine like terms: 9.797958971 + 1 = 10.797958971 w = 10.797958971 Simplifying w = 10.797958971Subproblem 2
w + -1 = -9.797958971 Simplifying w + -1 = -9.797958971 Reorder the terms: -1 + w = -9.797958971 Solving -1 + w = -9.797958971 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 = -9.797958971 + 1 Combine like terms: -1 + 1 = 0 0 + w = -9.797958971 + 1 w = -9.797958971 + 1 Combine like terms: -9.797958971 + 1 = -8.797958971 w = -8.797958971 Simplifying w = -8.797958971Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.797958971, -8.797958971}Solution
w = {10.797958971, -8.797958971}
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