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Simplifying -2w2 + 20w = -14 Reorder the terms: 20w + -2w2 = -14 Solving 20w + -2w2 = -14 Solving for variable 'w'. Reorder the terms: 14 + 20w + -2w2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + 20w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 10w + -1w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 10w + -1w2)' equal to zero and attempt to solve: Simplifying 7 + 10w + -1w2 = 0 Solving 7 + 10w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -10w + w2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -10w + 7 + w2 = 0 + 7 Reorder the terms: -7 + 7 + -10w + w2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10w + w2 = 0 + 7 -10w + w2 = 0 + 7 Combine like terms: 0 + 7 = 7 -10w + w2 = 7 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 = 7 + 25 Reorder the terms: 25 + -10w + w2 = 7 + 25 Combine like terms: 7 + 25 = 32 25 + -10w + w2 = 32 Factor a perfect square on the left side: (w + -5)(w + -5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (w + -5) equal to 5.656854249 and -5.656854249.Subproblem 1
w + -5 = 5.656854249 Simplifying w + -5 = 5.656854249 Reorder the terms: -5 + w = 5.656854249 Solving -5 + w = 5.656854249 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 = 5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + w = 5.656854249 + 5 w = 5.656854249 + 5 Combine like terms: 5.656854249 + 5 = 10.656854249 w = 10.656854249 Simplifying w = 10.656854249Subproblem 2
w + -5 = -5.656854249 Simplifying w + -5 = -5.656854249 Reorder the terms: -5 + w = -5.656854249 Solving -5 + w = -5.656854249 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 = -5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + w = -5.656854249 + 5 w = -5.656854249 + 5 Combine like terms: -5.656854249 + 5 = -0.656854249 w = -0.656854249 Simplifying w = -0.656854249Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.656854249, -0.656854249}Solution
w = {10.656854249, -0.656854249}
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