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Simplifying 2w2 + -20w + 2 = 0 Reorder the terms: 2 + -20w + 2w2 = 0 Solving 2 + -20w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -10w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -10w + w2)' equal to zero and attempt to solve: Simplifying 1 + -10w + w2 = 0 Solving 1 + -10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -10w + -1 + w2 = 0 + -1 Reorder the terms: 1 + -1 + -10w + w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10w + w2 = 0 + -1 -10w + w2 = 0 + -1 Combine like terms: 0 + -1 = -1 -10w + w2 = -1 The w term is -10w. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10w + 25 + w2 = -1 + 25 Reorder the terms: 25 + -10w + w2 = -1 + 25 Combine like terms: -1 + 25 = 24 25 + -10w + w2 = 24 Factor a perfect square on the left side: (w + -5)(w + -5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (w + -5) equal to 4.898979486 and -4.898979486.Subproblem 1
w + -5 = 4.898979486 Simplifying w + -5 = 4.898979486 Reorder the terms: -5 + w = 4.898979486 Solving -5 + w = 4.898979486 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + w = 4.898979486 + 5 w = 4.898979486 + 5 Combine like terms: 4.898979486 + 5 = 9.898979486 w = 9.898979486 Simplifying w = 9.898979486Subproblem 2
w + -5 = -4.898979486 Simplifying w + -5 = -4.898979486 Reorder the terms: -5 + w = -4.898979486 Solving -5 + w = -4.898979486 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = -4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + w = -4.898979486 + 5 w = -4.898979486 + 5 Combine like terms: -4.898979486 + 5 = 0.101020514 w = 0.101020514 Simplifying w = 0.101020514Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.898979486, 0.101020514}Solution
w = {9.898979486, 0.101020514}
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