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Simplifying w2 + -3w = 350 Reorder the terms: -3w + w2 = 350 Solving -3w + w2 = 350 Solving for variable 'w'. Reorder the terms: -350 + -3w + w2 = 350 + -350 Combine like terms: 350 + -350 = 0 -350 + -3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + -3w + 350 + w2 = 0 + 350 Reorder the terms: -350 + 350 + -3w + w2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + -3w + w2 = 0 + 350 -3w + w2 = 0 + 350 Combine like terms: 0 + 350 = 350 -3w + w2 = 350 The w term is -3w. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3w + 2.25 + w2 = 350 + 2.25 Reorder the terms: 2.25 + -3w + w2 = 350 + 2.25 Combine like terms: 350 + 2.25 = 352.25 2.25 + -3w + w2 = 352.25 Factor a perfect square on the left side: (w + -1.5)(w + -1.5) = 352.25 Calculate the square root of the right side: 18.768324379 Break this problem into two subproblems by setting (w + -1.5) equal to 18.768324379 and -18.768324379.Subproblem 1
w + -1.5 = 18.768324379 Simplifying w + -1.5 = 18.768324379 Reorder the terms: -1.5 + w = 18.768324379 Solving -1.5 + w = 18.768324379 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = 18.768324379 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = 18.768324379 + 1.5 w = 18.768324379 + 1.5 Combine like terms: 18.768324379 + 1.5 = 20.268324379 w = 20.268324379 Simplifying w = 20.268324379Subproblem 2
w + -1.5 = -18.768324379 Simplifying w + -1.5 = -18.768324379 Reorder the terms: -1.5 + w = -18.768324379 Solving -1.5 + w = -18.768324379 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = -18.768324379 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = -18.768324379 + 1.5 w = -18.768324379 + 1.5 Combine like terms: -18.768324379 + 1.5 = -17.268324379 w = -17.268324379 Simplifying w = -17.268324379Solution
The solution to the problem is based on the solutions from the subproblems. w = {20.268324379, -17.268324379}
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