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Simplifying 144 = w2 + 8w + 81 Reorder the terms: 144 = 81 + 8w + w2 Solving 144 = 81 + 8w + w2 Solving for variable 'w'. Combine like terms: 144 + -81 = 63 63 + -8w + -1w2 = 81 + 8w + w2 + -81 + -8w + -1w2 Reorder the terms: 63 + -8w + -1w2 = 81 + -81 + 8w + -8w + w2 + -1w2 Combine like terms: 81 + -81 = 0 63 + -8w + -1w2 = 0 + 8w + -8w + w2 + -1w2 63 + -8w + -1w2 = 8w + -8w + w2 + -1w2 Combine like terms: 8w + -8w = 0 63 + -8w + -1w2 = 0 + w2 + -1w2 63 + -8w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 63 + -8w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + 8w + w2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 8w + 63 + w2 = 0 + 63 Reorder the terms: -63 + 63 + 8w + w2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 8w + w2 = 0 + 63 8w + w2 = 0 + 63 Combine like terms: 0 + 63 = 63 8w + w2 = 63 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = 63 + 16 Reorder the terms: 16 + 8w + w2 = 63 + 16 Combine like terms: 63 + 16 = 79 16 + 8w + w2 = 79 Factor a perfect square on the left side: (w + 4)(w + 4) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (w + 4) equal to 8.888194417 and -8.888194417.Subproblem 1
w + 4 = 8.888194417 Simplifying w + 4 = 8.888194417 Reorder the terms: 4 + w = 8.888194417 Solving 4 + w = 8.888194417 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 8.888194417 + -4 Combine like terms: 4 + -4 = 0 0 + w = 8.888194417 + -4 w = 8.888194417 + -4 Combine like terms: 8.888194417 + -4 = 4.888194417 w = 4.888194417 Simplifying w = 4.888194417Subproblem 2
w + 4 = -8.888194417 Simplifying w + 4 = -8.888194417 Reorder the terms: 4 + w = -8.888194417 Solving 4 + w = -8.888194417 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -8.888194417 + -4 Combine like terms: 4 + -4 = 0 0 + w = -8.888194417 + -4 w = -8.888194417 + -4 Combine like terms: -8.888194417 + -4 = -12.888194417 w = -12.888194417 Simplifying w = -12.888194417Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.888194417, -12.888194417}
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