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Simplifying w2 + 2.3w = 1634.9 Reorder the terms: 2.3w + w2 = 1634.9 Solving 2.3w + w2 = 1634.9 Solving for variable 'w'. Reorder the terms: -1634.9 + 2.3w + w2 = 1634.9 + -1634.9 Combine like terms: 1634.9 + -1634.9 = 0.0 -1634.9 + 2.3w + w2 = 0.0 Begin completing the square. Move the constant term to the right: Add '1634.9' to each side of the equation. -1634.9 + 2.3w + 1634.9 + w2 = 0.0 + 1634.9 Reorder the terms: -1634.9 + 1634.9 + 2.3w + w2 = 0.0 + 1634.9 Combine like terms: -1634.9 + 1634.9 = 0.0 0.0 + 2.3w + w2 = 0.0 + 1634.9 2.3w + w2 = 0.0 + 1634.9 Combine like terms: 0.0 + 1634.9 = 1634.9 2.3w + w2 = 1634.9 The w term is 2.3w. Take half its coefficient (1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. 2.3w + 1.3225 + w2 = 1634.9 + 1.3225 Reorder the terms: 1.3225 + 2.3w + w2 = 1634.9 + 1.3225 Combine like terms: 1634.9 + 1.3225 = 1636.2225 1.3225 + 2.3w + w2 = 1636.2225 Factor a perfect square on the left side: (w + 1.15)(w + 1.15) = 1636.2225 Calculate the square root of the right side: 40.450247218 Break this problem into two subproblems by setting (w + 1.15) equal to 40.450247218 and -40.450247218.Subproblem 1
w + 1.15 = 40.450247218 Simplifying w + 1.15 = 40.450247218 Reorder the terms: 1.15 + w = 40.450247218 Solving 1.15 + w = 40.450247218 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + w = 40.450247218 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + w = 40.450247218 + -1.15 w = 40.450247218 + -1.15 Combine like terms: 40.450247218 + -1.15 = 39.300247218 w = 39.300247218 Simplifying w = 39.300247218Subproblem 2
w + 1.15 = -40.450247218 Simplifying w + 1.15 = -40.450247218 Reorder the terms: 1.15 + w = -40.450247218 Solving 1.15 + w = -40.450247218 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + w = -40.450247218 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + w = -40.450247218 + -1.15 w = -40.450247218 + -1.15 Combine like terms: -40.450247218 + -1.15 = -41.600247218 w = -41.600247218 Simplifying w = -41.600247218Solution
The solution to the problem is based on the solutions from the subproblems. w = {39.300247218, -41.600247218}
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