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Simplifying w2 + -13w = 36 Reorder the terms: -13w + w2 = 36 Solving -13w + w2 = 36 Solving for variable 'w'. Reorder the terms: -36 + -13w + w2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -13w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -13w + 36 + w2 = 0 + 36 Reorder the terms: -36 + 36 + -13w + w2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -13w + w2 = 0 + 36 -13w + w2 = 0 + 36 Combine like terms: 0 + 36 = 36 -13w + w2 = 36 The w term is -13w. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13w + 42.25 + w2 = 36 + 42.25 Reorder the terms: 42.25 + -13w + w2 = 36 + 42.25 Combine like terms: 36 + 42.25 = 78.25 42.25 + -13w + w2 = 78.25 Factor a perfect square on the left side: (w + -6.5)(w + -6.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (w + -6.5) equal to 8.845903006 and -8.845903006.Subproblem 1
w + -6.5 = 8.845903006 Simplifying w + -6.5 = 8.845903006 Reorder the terms: -6.5 + w = 8.845903006 Solving -6.5 + w = 8.845903006 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + w = 8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = 8.845903006 + 6.5 w = 8.845903006 + 6.5 Combine like terms: 8.845903006 + 6.5 = 15.345903006 w = 15.345903006 Simplifying w = 15.345903006Subproblem 2
w + -6.5 = -8.845903006 Simplifying w + -6.5 = -8.845903006 Reorder the terms: -6.5 + w = -8.845903006 Solving -6.5 + w = -8.845903006 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + w = -8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = -8.845903006 + 6.5 w = -8.845903006 + 6.5 Combine like terms: -8.845903006 + 6.5 = -2.345903006 w = -2.345903006 Simplifying w = -2.345903006Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.345903006, -2.345903006}
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