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Simplifying -2w2 + 28w = 10 Reorder the terms: 28w + -2w2 = 10 Solving 28w + -2w2 = 10 Solving for variable 'w'. Reorder the terms: -10 + 28w + -2w2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 28w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 14w + -1w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 14w + -1w2)' equal to zero and attempt to solve: Simplifying -5 + 14w + -1w2 = 0 Solving -5 + 14w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -14w + w2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -14w + -5 + w2 = 0 + -5 Reorder the terms: 5 + -5 + -14w + w2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -14w + w2 = 0 + -5 -14w + w2 = 0 + -5 Combine like terms: 0 + -5 = -5 -14w + w2 = -5 The w term is -14w. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14w + 49 + w2 = -5 + 49 Reorder the terms: 49 + -14w + w2 = -5 + 49 Combine like terms: -5 + 49 = 44 49 + -14w + w2 = 44 Factor a perfect square on the left side: (w + -7)(w + -7) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (w + -7) equal to 6.633249581 and -6.633249581.Subproblem 1
w + -7 = 6.633249581 Simplifying w + -7 = 6.633249581 Reorder the terms: -7 + w = 6.633249581 Solving -7 + w = 6.633249581 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + w = 6.633249581 + 7 Combine like terms: -7 + 7 = 0 0 + w = 6.633249581 + 7 w = 6.633249581 + 7 Combine like terms: 6.633249581 + 7 = 13.633249581 w = 13.633249581 Simplifying w = 13.633249581Subproblem 2
w + -7 = -6.633249581 Simplifying w + -7 = -6.633249581 Reorder the terms: -7 + w = -6.633249581 Solving -7 + w = -6.633249581 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + w = -6.633249581 + 7 Combine like terms: -7 + 7 = 0 0 + w = -6.633249581 + 7 w = -6.633249581 + 7 Combine like terms: -6.633249581 + 7 = 0.366750419 w = 0.366750419 Simplifying w = 0.366750419Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.633249581, 0.366750419}Solution
w = {13.633249581, 0.366750419}
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