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Simplifying 2W2 + -40W + 82 = 0 Reorder the terms: 82 + -40W + 2W2 = 0 Solving 82 + -40W + 2W2 = 0 Solving for variable 'W'. Factor out the Greatest Common Factor (GCF), '2'. 2(41 + -20W + W2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + -20W + W2)' equal to zero and attempt to solve: Simplifying 41 + -20W + W2 = 0 Solving 41 + -20W + W2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -20W + -41 + W2 = 0 + -41 Reorder the terms: 41 + -41 + -20W + W2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -20W + W2 = 0 + -41 -20W + W2 = 0 + -41 Combine like terms: 0 + -41 = -41 -20W + W2 = -41 The W term is -20W. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20W + 100 + W2 = -41 + 100 Reorder the terms: 100 + -20W + W2 = -41 + 100 Combine like terms: -41 + 100 = 59 100 + -20W + W2 = 59 Factor a perfect square on the left side: (W + -10)(W + -10) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (W + -10) equal to 7.681145748 and -7.681145748.Subproblem 1
W + -10 = 7.681145748 Simplifying W + -10 = 7.681145748 Reorder the terms: -10 + W = 7.681145748 Solving -10 + W = 7.681145748 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + W = 7.681145748 + 10 Combine like terms: -10 + 10 = 0 0 + W = 7.681145748 + 10 W = 7.681145748 + 10 Combine like terms: 7.681145748 + 10 = 17.681145748 W = 17.681145748 Simplifying W = 17.681145748Subproblem 2
W + -10 = -7.681145748 Simplifying W + -10 = -7.681145748 Reorder the terms: -10 + W = -7.681145748 Solving -10 + W = -7.681145748 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + W = -7.681145748 + 10 Combine like terms: -10 + 10 = 0 0 + W = -7.681145748 + 10 W = -7.681145748 + 10 Combine like terms: -7.681145748 + 10 = 2.318854252 W = 2.318854252 Simplifying W = 2.318854252Solution
The solution to the problem is based on the solutions from the subproblems. W = {17.681145748, 2.318854252}Solution
W = {17.681145748, 2.318854252}
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