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Simplifying 16w2 + 17w + -14 = 0 Reorder the terms: -14 + 17w + 16w2 = 0 Solving -14 + 17w + 16w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.875 + 1.0625w + w2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 1.0625w + 0.875 + w2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 1.0625w + w2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 1.0625w + w2 = 0 + 0.875 1.0625w + w2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 1.0625w + w2 = 0.875 The w term is 1.0625w. Take half its coefficient (0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. 1.0625w + 0.2822265625 + w2 = 0.875 + 0.2822265625 Reorder the terms: 0.2822265625 + 1.0625w + w2 = 0.875 + 0.2822265625 Combine like terms: 0.875 + 0.2822265625 = 1.1572265625 0.2822265625 + 1.0625w + w2 = 1.1572265625 Factor a perfect square on the left side: (w + 0.53125)(w + 0.53125) = 1.1572265625 Calculate the square root of the right side: 1.075744655 Break this problem into two subproblems by setting (w + 0.53125) equal to 1.075744655 and -1.075744655.Subproblem 1
w + 0.53125 = 1.075744655 Simplifying w + 0.53125 = 1.075744655 Reorder the terms: 0.53125 + w = 1.075744655 Solving 0.53125 + w = 1.075744655 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + w = 1.075744655 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + w = 1.075744655 + -0.53125 w = 1.075744655 + -0.53125 Combine like terms: 1.075744655 + -0.53125 = 0.544494655 w = 0.544494655 Simplifying w = 0.544494655Subproblem 2
w + 0.53125 = -1.075744655 Simplifying w + 0.53125 = -1.075744655 Reorder the terms: 0.53125 + w = -1.075744655 Solving 0.53125 + w = -1.075744655 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + w = -1.075744655 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + w = -1.075744655 + -0.53125 w = -1.075744655 + -0.53125 Combine like terms: -1.075744655 + -0.53125 = -1.606994655 w = -1.606994655 Simplifying w = -1.606994655Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.544494655, -1.606994655}
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