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Simplifying (w + -3) * w = 346 Reorder the terms: (-3 + w) * w = 346 Reorder the terms for easier multiplication: w(-3 + w) = 346 (-3 * w + w * w) = 346 (-3w + w2) = 346 Solving -3w + w2 = 346 Solving for variable 'w'. Reorder the terms: -346 + -3w + w2 = 346 + -346 Combine like terms: 346 + -346 = 0 -346 + -3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '346' to each side of the equation. -346 + -3w + 346 + w2 = 0 + 346 Reorder the terms: -346 + 346 + -3w + w2 = 0 + 346 Combine like terms: -346 + 346 = 0 0 + -3w + w2 = 0 + 346 -3w + w2 = 0 + 346 Combine like terms: 0 + 346 = 346 -3w + w2 = 346 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 = 346 + 2.25 Reorder the terms: 2.25 + -3w + w2 = 346 + 2.25 Combine like terms: 346 + 2.25 = 348.25 2.25 + -3w + w2 = 348.25 Factor a perfect square on the left side: (w + -1.5)(w + -1.5) = 348.25 Calculate the square root of the right side: 18.661457607 Break this problem into two subproblems by setting (w + -1.5) equal to 18.661457607 and -18.661457607.Subproblem 1
w + -1.5 = 18.661457607 Simplifying w + -1.5 = 18.661457607 Reorder the terms: -1.5 + w = 18.661457607 Solving -1.5 + w = 18.661457607 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 = 18.661457607 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = 18.661457607 + 1.5 w = 18.661457607 + 1.5 Combine like terms: 18.661457607 + 1.5 = 20.161457607 w = 20.161457607 Simplifying w = 20.161457607Subproblem 2
w + -1.5 = -18.661457607 Simplifying w + -1.5 = -18.661457607 Reorder the terms: -1.5 + w = -18.661457607 Solving -1.5 + w = -18.661457607 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 = -18.661457607 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = -18.661457607 + 1.5 w = -18.661457607 + 1.5 Combine like terms: -18.661457607 + 1.5 = -17.161457607 w = -17.161457607 Simplifying w = -17.161457607Solution
The solution to the problem is based on the solutions from the subproblems. w = {20.161457607, -17.161457607}
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