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Simplifying w2 + -4w + -240 = 0 Reorder the terms: -240 + -4w + w2 = 0 Solving -240 + -4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + -4w + 240 + w2 = 0 + 240 Reorder the terms: -240 + 240 + -4w + w2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -4w + w2 = 0 + 240 -4w + w2 = 0 + 240 Combine like terms: 0 + 240 = 240 -4w + w2 = 240 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 240 + 4 Reorder the terms: 4 + -4w + w2 = 240 + 4 Combine like terms: 240 + 4 = 244 4 + -4w + w2 = 244 Factor a perfect square on the left side: (w + -2)(w + -2) = 244 Calculate the square root of the right side: 15.620499352 Break this problem into two subproblems by setting (w + -2) equal to 15.620499352 and -15.620499352.Subproblem 1
w + -2 = 15.620499352 Simplifying w + -2 = 15.620499352 Reorder the terms: -2 + w = 15.620499352 Solving -2 + w = 15.620499352 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 15.620499352 + 2 Combine like terms: -2 + 2 = 0 0 + w = 15.620499352 + 2 w = 15.620499352 + 2 Combine like terms: 15.620499352 + 2 = 17.620499352 w = 17.620499352 Simplifying w = 17.620499352Subproblem 2
w + -2 = -15.620499352 Simplifying w + -2 = -15.620499352 Reorder the terms: -2 + w = -15.620499352 Solving -2 + w = -15.620499352 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -15.620499352 + 2 Combine like terms: -2 + 2 = 0 0 + w = -15.620499352 + 2 w = -15.620499352 + 2 Combine like terms: -15.620499352 + 2 = -13.620499352 w = -13.620499352 Simplifying w = -13.620499352Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.620499352, -13.620499352}
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