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Simplifying 2w2 + 14w + -480 = 0 Reorder the terms: -480 + 14w + 2w2 = 0 Solving -480 + 14w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-240 + 7w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-240 + 7w + w2)' equal to zero and attempt to solve: Simplifying -240 + 7w + w2 = 0 Solving -240 + 7w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 7w + 240 + w2 = 0 + 240 Reorder the terms: -240 + 240 + 7w + w2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 7w + w2 = 0 + 240 7w + w2 = 0 + 240 Combine like terms: 0 + 240 = 240 7w + w2 = 240 The w term is 7w. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7w + 12.25 + w2 = 240 + 12.25 Reorder the terms: 12.25 + 7w + w2 = 240 + 12.25 Combine like terms: 240 + 12.25 = 252.25 12.25 + 7w + w2 = 252.25 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 252.25 Calculate the square root of the right side: 15.882380174 Break this problem into two subproblems by setting (w + 3.5) equal to 15.882380174 and -15.882380174.Subproblem 1
w + 3.5 = 15.882380174 Simplifying w + 3.5 = 15.882380174 Reorder the terms: 3.5 + w = 15.882380174 Solving 3.5 + w = 15.882380174 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = 15.882380174 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 15.882380174 + -3.5 w = 15.882380174 + -3.5 Combine like terms: 15.882380174 + -3.5 = 12.382380174 w = 12.382380174 Simplifying w = 12.382380174Subproblem 2
w + 3.5 = -15.882380174 Simplifying w + 3.5 = -15.882380174 Reorder the terms: 3.5 + w = -15.882380174 Solving 3.5 + w = -15.882380174 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = -15.882380174 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -15.882380174 + -3.5 w = -15.882380174 + -3.5 Combine like terms: -15.882380174 + -3.5 = -19.382380174 w = -19.382380174 Simplifying w = -19.382380174Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.382380174, -19.382380174}Solution
w = {12.382380174, -19.382380174}
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