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Simplifying 0 = w2 + 3w + -196 Reorder the terms: 0 = -196 + 3w + w2 Solving 0 = -196 + 3w + w2 Solving for variable 'w'. Combine like terms: 0 + 196 = 196 196 + -3w + -1w2 = -196 + 3w + w2 + 196 + -3w + -1w2 Reorder the terms: 196 + -3w + -1w2 = -196 + 196 + 3w + -3w + w2 + -1w2 Combine like terms: -196 + 196 = 0 196 + -3w + -1w2 = 0 + 3w + -3w + w2 + -1w2 196 + -3w + -1w2 = 3w + -3w + w2 + -1w2 Combine like terms: 3w + -3w = 0 196 + -3w + -1w2 = 0 + w2 + -1w2 196 + -3w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 196 + -3w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -196 + 3w + w2 = 0 Move the constant term to the right: Add '196' to each side of the equation. -196 + 3w + 196 + w2 = 0 + 196 Reorder the terms: -196 + 196 + 3w + w2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 3w + w2 = 0 + 196 3w + w2 = 0 + 196 Combine like terms: 0 + 196 = 196 3w + w2 = 196 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 = 196 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 196 + 2.25 Combine like terms: 196 + 2.25 = 198.25 2.25 + 3w + w2 = 198.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 198.25 Calculate the square root of the right side: 14.08012784 Break this problem into two subproblems by setting (w + 1.5) equal to 14.08012784 and -14.08012784.Subproblem 1
w + 1.5 = 14.08012784 Simplifying w + 1.5 = 14.08012784 Reorder the terms: 1.5 + w = 14.08012784 Solving 1.5 + w = 14.08012784 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 = 14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 14.08012784 + -1.5 w = 14.08012784 + -1.5 Combine like terms: 14.08012784 + -1.5 = 12.58012784 w = 12.58012784 Simplifying w = 12.58012784Subproblem 2
w + 1.5 = -14.08012784 Simplifying w + 1.5 = -14.08012784 Reorder the terms: 1.5 + w = -14.08012784 Solving 1.5 + w = -14.08012784 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 = -14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -14.08012784 + -1.5 w = -14.08012784 + -1.5 Combine like terms: -14.08012784 + -1.5 = -15.58012784 w = -15.58012784 Simplifying w = -15.58012784Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.58012784, -15.58012784}
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