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Simplifying 5w2 + -10w + -162 = 0 Reorder the terms: -162 + -10w + 5w2 = 0 Solving -162 + -10w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -32.4 + -2w + w2 = 0 Move the constant term to the right: Add '32.4' to each side of the equation. -32.4 + -2w + 32.4 + w2 = 0 + 32.4 Reorder the terms: -32.4 + 32.4 + -2w + w2 = 0 + 32.4 Combine like terms: -32.4 + 32.4 = 0.0 0.0 + -2w + w2 = 0 + 32.4 -2w + w2 = 0 + 32.4 Combine like terms: 0 + 32.4 = 32.4 -2w + w2 = 32.4 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 32.4 + 1 Reorder the terms: 1 + -2w + w2 = 32.4 + 1 Combine like terms: 32.4 + 1 = 33.4 1 + -2w + w2 = 33.4 Factor a perfect square on the left side: (w + -1)(w + -1) = 33.4 Calculate the square root of the right side: 5.779273311 Break this problem into two subproblems by setting (w + -1) equal to 5.779273311 and -5.779273311.Subproblem 1
w + -1 = 5.779273311 Simplifying w + -1 = 5.779273311 Reorder the terms: -1 + w = 5.779273311 Solving -1 + w = 5.779273311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 5.779273311 + 1 Combine like terms: -1 + 1 = 0 0 + w = 5.779273311 + 1 w = 5.779273311 + 1 Combine like terms: 5.779273311 + 1 = 6.779273311 w = 6.779273311 Simplifying w = 6.779273311Subproblem 2
w + -1 = -5.779273311 Simplifying w + -1 = -5.779273311 Reorder the terms: -1 + w = -5.779273311 Solving -1 + w = -5.779273311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -5.779273311 + 1 Combine like terms: -1 + 1 = 0 0 + w = -5.779273311 + 1 w = -5.779273311 + 1 Combine like terms: -5.779273311 + 1 = -4.779273311 w = -4.779273311 Simplifying w = -4.779273311Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.779273311, -4.779273311}
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