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Simplifying w2 + -19w + -36 = 0 Reorder the terms: -36 + -19w + w2 = 0 Solving -36 + -19w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -19w + 36 + w2 = 0 + 36 Reorder the terms: -36 + 36 + -19w + w2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -19w + w2 = 0 + 36 -19w + w2 = 0 + 36 Combine like terms: 0 + 36 = 36 -19w + w2 = 36 The w term is -19w. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19w + 90.25 + w2 = 36 + 90.25 Reorder the terms: 90.25 + -19w + w2 = 36 + 90.25 Combine like terms: 36 + 90.25 = 126.25 90.25 + -19w + w2 = 126.25 Factor a perfect square on the left side: (w + -9.5)(w + -9.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (w + -9.5) equal to 11.236102527 and -11.236102527.Subproblem 1
w + -9.5 = 11.236102527 Simplifying w + -9.5 = 11.236102527 Reorder the terms: -9.5 + w = 11.236102527 Solving -9.5 + w = 11.236102527 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + w = 11.236102527 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + w = 11.236102527 + 9.5 w = 11.236102527 + 9.5 Combine like terms: 11.236102527 + 9.5 = 20.736102527 w = 20.736102527 Simplifying w = 20.736102527Subproblem 2
w + -9.5 = -11.236102527 Simplifying w + -9.5 = -11.236102527 Reorder the terms: -9.5 + w = -11.236102527 Solving -9.5 + w = -11.236102527 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + w = -11.236102527 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + w = -11.236102527 + 9.5 w = -11.236102527 + 9.5 Combine like terms: -11.236102527 + 9.5 = -1.736102527 w = -1.736102527 Simplifying w = -1.736102527Solution
The solution to the problem is based on the solutions from the subproblems. w = {20.736102527, -1.736102527}
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