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Simplifying 31w + 5w2 = 31 Solving 31w + 5w2 = 31 Solving for variable 'w'. Reorder the terms: -31 + 31w + 5w2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + 31w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.2 + 6.2w + w2 = 0 Move the constant term to the right: Add '6.2' to each side of the equation. -6.2 + 6.2w + 6.2 + w2 = 0 + 6.2 Reorder the terms: -6.2 + 6.2 + 6.2w + w2 = 0 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + 6.2w + w2 = 0 + 6.2 6.2w + w2 = 0 + 6.2 Combine like terms: 0 + 6.2 = 6.2 6.2w + w2 = 6.2 The w term is 6.2w. Take half its coefficient (3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. 6.2w + 9.61 + w2 = 6.2 + 9.61 Reorder the terms: 9.61 + 6.2w + w2 = 6.2 + 9.61 Combine like terms: 6.2 + 9.61 = 15.81 9.61 + 6.2w + w2 = 15.81 Factor a perfect square on the left side: (w + 3.1)(w + 3.1) = 15.81 Calculate the square root of the right side: 3.97617907 Break this problem into two subproblems by setting (w + 3.1) equal to 3.97617907 and -3.97617907.Subproblem 1
w + 3.1 = 3.97617907 Simplifying w + 3.1 = 3.97617907 Reorder the terms: 3.1 + w = 3.97617907 Solving 3.1 + w = 3.97617907 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + w = 3.97617907 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + w = 3.97617907 + -3.1 w = 3.97617907 + -3.1 Combine like terms: 3.97617907 + -3.1 = 0.87617907 w = 0.87617907 Simplifying w = 0.87617907Subproblem 2
w + 3.1 = -3.97617907 Simplifying w + 3.1 = -3.97617907 Reorder the terms: 3.1 + w = -3.97617907 Solving 3.1 + w = -3.97617907 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + w = -3.97617907 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + w = -3.97617907 + -3.1 w = -3.97617907 + -3.1 Combine like terms: -3.97617907 + -3.1 = -7.07617907 w = -7.07617907 Simplifying w = -7.07617907Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.87617907, -7.07617907}
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