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Simplifying 28w2 + 60w + -10440 = 0 Reorder the terms: -10440 + 60w + 28w2 = 0 Solving -10440 + 60w + 28w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2610 + 15w + 7w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2610 + 15w + 7w2)' equal to zero and attempt to solve: Simplifying -2610 + 15w + 7w2 = 0 Solving -2610 + 15w + 7w2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -372.8571429 + 2.142857143w + w2 = 0 Move the constant term to the right: Add '372.8571429' to each side of the equation. -372.8571429 + 2.142857143w + 372.8571429 + w2 = 0 + 372.8571429 Reorder the terms: -372.8571429 + 372.8571429 + 2.142857143w + w2 = 0 + 372.8571429 Combine like terms: -372.8571429 + 372.8571429 = 0.0000000 0.0000000 + 2.142857143w + w2 = 0 + 372.8571429 2.142857143w + w2 = 0 + 372.8571429 Combine like terms: 0 + 372.8571429 = 372.8571429 2.142857143w + w2 = 372.8571429 The w term is 2.142857143w. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143w + 1.147959185 + w2 = 372.8571429 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143w + w2 = 372.8571429 + 1.147959185 Combine like terms: 372.8571429 + 1.147959185 = 374.005102085 1.147959185 + 2.142857143w + w2 = 374.005102085 Factor a perfect square on the left side: (w + 1.071428572)(w + 1.071428572) = 374.005102085 Calculate the square root of the right side: 19.339211517 Break this problem into two subproblems by setting (w + 1.071428572) equal to 19.339211517 and -19.339211517.Subproblem 1
w + 1.071428572 = 19.339211517 Simplifying w + 1.071428572 = 19.339211517 Reorder the terms: 1.071428572 + w = 19.339211517 Solving 1.071428572 + w = 19.339211517 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + w = 19.339211517 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + w = 19.339211517 + -1.071428572 w = 19.339211517 + -1.071428572 Combine like terms: 19.339211517 + -1.071428572 = 18.267782945 w = 18.267782945 Simplifying w = 18.267782945Subproblem 2
w + 1.071428572 = -19.339211517 Simplifying w + 1.071428572 = -19.339211517 Reorder the terms: 1.071428572 + w = -19.339211517 Solving 1.071428572 + w = -19.339211517 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + w = -19.339211517 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + w = -19.339211517 + -1.071428572 w = -19.339211517 + -1.071428572 Combine like terms: -19.339211517 + -1.071428572 = -20.410640089 w = -20.410640089 Simplifying w = -20.410640089Solution
The solution to the problem is based on the solutions from the subproblems. w = {18.267782945, -20.410640089}Solution
w = {18.267782945, -20.410640089}
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