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Simplifying w2 + 8w = 340 Reorder the terms: 8w + w2 = 340 Solving 8w + w2 = 340 Solving for variable 'w'. Reorder the terms: -340 + 8w + w2 = 340 + -340 Combine like terms: 340 + -340 = 0 -340 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '340' to each side of the equation. -340 + 8w + 340 + w2 = 0 + 340 Reorder the terms: -340 + 340 + 8w + w2 = 0 + 340 Combine like terms: -340 + 340 = 0 0 + 8w + w2 = 0 + 340 8w + w2 = 0 + 340 Combine like terms: 0 + 340 = 340 8w + w2 = 340 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = 340 + 16 Reorder the terms: 16 + 8w + w2 = 340 + 16 Combine like terms: 340 + 16 = 356 16 + 8w + w2 = 356 Factor a perfect square on the left side: (w + 4)(w + 4) = 356 Calculate the square root of the right side: 18.867962264 Break this problem into two subproblems by setting (w + 4) equal to 18.867962264 and -18.867962264.Subproblem 1
w + 4 = 18.867962264 Simplifying w + 4 = 18.867962264 Reorder the terms: 4 + w = 18.867962264 Solving 4 + w = 18.867962264 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 18.867962264 + -4 Combine like terms: 4 + -4 = 0 0 + w = 18.867962264 + -4 w = 18.867962264 + -4 Combine like terms: 18.867962264 + -4 = 14.867962264 w = 14.867962264 Simplifying w = 14.867962264Subproblem 2
w + 4 = -18.867962264 Simplifying w + 4 = -18.867962264 Reorder the terms: 4 + w = -18.867962264 Solving 4 + w = -18.867962264 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -18.867962264 + -4 Combine like terms: 4 + -4 = 0 0 + w = -18.867962264 + -4 w = -18.867962264 + -4 Combine like terms: -18.867962264 + -4 = -22.867962264 w = -22.867962264 Simplifying w = -22.867962264Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.867962264, -22.867962264}
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