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Simplifying w2 + 4w + -336 = 0 Reorder the terms: -336 + 4w + w2 = 0 Solving -336 + 4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '336' to each side of the equation. -336 + 4w + 336 + w2 = 0 + 336 Reorder the terms: -336 + 336 + 4w + w2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + 4w + w2 = 0 + 336 4w + w2 = 0 + 336 Combine like terms: 0 + 336 = 336 4w + w2 = 336 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 = 336 + 4 Reorder the terms: 4 + 4w + w2 = 336 + 4 Combine like terms: 336 + 4 = 340 4 + 4w + w2 = 340 Factor a perfect square on the left side: (w + 2)(w + 2) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (w + 2) equal to 18.439088915 and -18.439088915.Subproblem 1
w + 2 = 18.439088915 Simplifying w + 2 = 18.439088915 Reorder the terms: 2 + w = 18.439088915 Solving 2 + w = 18.439088915 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 = 18.439088915 + -2 Combine like terms: 2 + -2 = 0 0 + w = 18.439088915 + -2 w = 18.439088915 + -2 Combine like terms: 18.439088915 + -2 = 16.439088915 w = 16.439088915 Simplifying w = 16.439088915Subproblem 2
w + 2 = -18.439088915 Simplifying w + 2 = -18.439088915 Reorder the terms: 2 + w = -18.439088915 Solving 2 + w = -18.439088915 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 = -18.439088915 + -2 Combine like terms: 2 + -2 = 0 0 + w = -18.439088915 + -2 w = -18.439088915 + -2 Combine like terms: -18.439088915 + -2 = -20.439088915 w = -20.439088915 Simplifying w = -20.439088915Solution
The solution to the problem is based on the solutions from the subproblems. w = {16.439088915, -20.439088915}
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