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Simplifying 4w2 + 37w + 53 = 0 Reorder the terms: 53 + 37w + 4w2 = 0 Solving 53 + 37w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 13.25 + 9.25w + w2 = 0 Move the constant term to the right: Add '-13.25' to each side of the equation. 13.25 + 9.25w + -13.25 + w2 = 0 + -13.25 Reorder the terms: 13.25 + -13.25 + 9.25w + w2 = 0 + -13.25 Combine like terms: 13.25 + -13.25 = 0.00 0.00 + 9.25w + w2 = 0 + -13.25 9.25w + w2 = 0 + -13.25 Combine like terms: 0 + -13.25 = -13.25 9.25w + w2 = -13.25 The w term is 9.25w. Take half its coefficient (4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. 9.25w + 21.390625 + w2 = -13.25 + 21.390625 Reorder the terms: 21.390625 + 9.25w + w2 = -13.25 + 21.390625 Combine like terms: -13.25 + 21.390625 = 8.140625 21.390625 + 9.25w + w2 = 8.140625 Factor a perfect square on the left side: (w + 4.625)(w + 4.625) = 8.140625 Calculate the square root of the right side: 2.853178053 Break this problem into two subproblems by setting (w + 4.625) equal to 2.853178053 and -2.853178053.Subproblem 1
w + 4.625 = 2.853178053 Simplifying w + 4.625 = 2.853178053 Reorder the terms: 4.625 + w = 2.853178053 Solving 4.625 + w = 2.853178053 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + w = 2.853178053 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + w = 2.853178053 + -4.625 w = 2.853178053 + -4.625 Combine like terms: 2.853178053 + -4.625 = -1.771821947 w = -1.771821947 Simplifying w = -1.771821947Subproblem 2
w + 4.625 = -2.853178053 Simplifying w + 4.625 = -2.853178053 Reorder the terms: 4.625 + w = -2.853178053 Solving 4.625 + w = -2.853178053 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.625' to each side of the equation. 4.625 + -4.625 + w = -2.853178053 + -4.625 Combine like terms: 4.625 + -4.625 = 0.000 0.000 + w = -2.853178053 + -4.625 w = -2.853178053 + -4.625 Combine like terms: -2.853178053 + -4.625 = -7.478178053 w = -7.478178053 Simplifying w = -7.478178053Solution
The solution to the problem is based on the solutions from the subproblems. w = {-1.771821947, -7.478178053}
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