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Simplifying w2 + -70w + -140 = 0 Reorder the terms: -140 + -70w + w2 = 0 Solving -140 + -70w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -70w + 140 + w2 = 0 + 140 Reorder the terms: -140 + 140 + -70w + w2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -70w + w2 = 0 + 140 -70w + w2 = 0 + 140 Combine like terms: 0 + 140 = 140 -70w + w2 = 140 The w term is -70w. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70w + 1225 + w2 = 140 + 1225 Reorder the terms: 1225 + -70w + w2 = 140 + 1225 Combine like terms: 140 + 1225 = 1365 1225 + -70w + w2 = 1365 Factor a perfect square on the left side: (w + -35)(w + -35) = 1365 Calculate the square root of the right side: 36.945906404 Break this problem into two subproblems by setting (w + -35) equal to 36.945906404 and -36.945906404.Subproblem 1
w + -35 = 36.945906404 Simplifying w + -35 = 36.945906404 Reorder the terms: -35 + w = 36.945906404 Solving -35 + w = 36.945906404 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + w = 36.945906404 + 35 Combine like terms: -35 + 35 = 0 0 + w = 36.945906404 + 35 w = 36.945906404 + 35 Combine like terms: 36.945906404 + 35 = 71.945906404 w = 71.945906404 Simplifying w = 71.945906404Subproblem 2
w + -35 = -36.945906404 Simplifying w + -35 = -36.945906404 Reorder the terms: -35 + w = -36.945906404 Solving -35 + w = -36.945906404 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + w = -36.945906404 + 35 Combine like terms: -35 + 35 = 0 0 + w = -36.945906404 + 35 w = -36.945906404 + 35 Combine like terms: -36.945906404 + 35 = -1.945906404 w = -1.945906404 Simplifying w = -1.945906404Solution
The solution to the problem is based on the solutions from the subproblems. w = {71.945906404, -1.945906404}
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