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Simplifying w2 + -29w = 270 Reorder the terms: -29w + w2 = 270 Solving -29w + w2 = 270 Solving for variable 'w'. Reorder the terms: -270 + -29w + w2 = 270 + -270 Combine like terms: 270 + -270 = 0 -270 + -29w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + -29w + 270 + w2 = 0 + 270 Reorder the terms: -270 + 270 + -29w + w2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + -29w + w2 = 0 + 270 -29w + w2 = 0 + 270 Combine like terms: 0 + 270 = 270 -29w + w2 = 270 The w term is -29w. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29w + 210.25 + w2 = 270 + 210.25 Reorder the terms: 210.25 + -29w + w2 = 270 + 210.25 Combine like terms: 270 + 210.25 = 480.25 210.25 + -29w + w2 = 480.25 Factor a perfect square on the left side: (w + -14.5)(w + -14.5) = 480.25 Calculate the square root of the right side: 21.914607001 Break this problem into two subproblems by setting (w + -14.5) equal to 21.914607001 and -21.914607001.Subproblem 1
w + -14.5 = 21.914607001 Simplifying w + -14.5 = 21.914607001 Reorder the terms: -14.5 + w = 21.914607001 Solving -14.5 + w = 21.914607001 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + w = 21.914607001 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + w = 21.914607001 + 14.5 w = 21.914607001 + 14.5 Combine like terms: 21.914607001 + 14.5 = 36.414607001 w = 36.414607001 Simplifying w = 36.414607001Subproblem 2
w + -14.5 = -21.914607001 Simplifying w + -14.5 = -21.914607001 Reorder the terms: -14.5 + w = -21.914607001 Solving -14.5 + w = -21.914607001 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + w = -21.914607001 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + w = -21.914607001 + 14.5 w = -21.914607001 + 14.5 Combine like terms: -21.914607001 + 14.5 = -7.414607001 w = -7.414607001 Simplifying w = -7.414607001Solution
The solution to the problem is based on the solutions from the subproblems. w = {36.414607001, -7.414607001}
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