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Simplifying w2 + 200w + -1875 = 0 Reorder the terms: -1875 + 200w + w2 = 0 Solving -1875 + 200w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '1875' to each side of the equation. -1875 + 200w + 1875 + w2 = 0 + 1875 Reorder the terms: -1875 + 1875 + 200w + w2 = 0 + 1875 Combine like terms: -1875 + 1875 = 0 0 + 200w + w2 = 0 + 1875 200w + w2 = 0 + 1875 Combine like terms: 0 + 1875 = 1875 200w + w2 = 1875 The w term is 200w. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200w + 10000 + w2 = 1875 + 10000 Reorder the terms: 10000 + 200w + w2 = 1875 + 10000 Combine like terms: 1875 + 10000 = 11875 10000 + 200w + w2 = 11875 Factor a perfect square on the left side: (w + 100)(w + 100) = 11875 Calculate the square root of the right side: 108.972473589 Break this problem into two subproblems by setting (w + 100) equal to 108.972473589 and -108.972473589.Subproblem 1
w + 100 = 108.972473589 Simplifying w + 100 = 108.972473589 Reorder the terms: 100 + w = 108.972473589 Solving 100 + w = 108.972473589 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + w = 108.972473589 + -100 Combine like terms: 100 + -100 = 0 0 + w = 108.972473589 + -100 w = 108.972473589 + -100 Combine like terms: 108.972473589 + -100 = 8.972473589 w = 8.972473589 Simplifying w = 8.972473589Subproblem 2
w + 100 = -108.972473589 Simplifying w + 100 = -108.972473589 Reorder the terms: 100 + w = -108.972473589 Solving 100 + w = -108.972473589 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + w = -108.972473589 + -100 Combine like terms: 100 + -100 = 0 0 + w = -108.972473589 + -100 w = -108.972473589 + -100 Combine like terms: -108.972473589 + -100 = -208.972473589 w = -208.972473589 Simplifying w = -208.972473589Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.972473589, -208.972473589}
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