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Simplifying w(w + 4) = 144 Reorder the terms: w(4 + w) = 144 (4 * w + w * w) = 144 (4w + w2) = 144 Solving 4w + w2 = 144 Solving for variable 'w'. Reorder the terms: -144 + 4w + w2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 4w + 144 + w2 = 0 + 144 Reorder the terms: -144 + 144 + 4w + w2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 4w + w2 = 0 + 144 4w + w2 = 0 + 144 Combine like terms: 0 + 144 = 144 4w + w2 = 144 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 144 + 4 Reorder the terms: 4 + 4w + w2 = 144 + 4 Combine like terms: 144 + 4 = 148 4 + 4w + w2 = 148 Factor a perfect square on the left side: (w + 2)(w + 2) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (w + 2) equal to 12.165525061 and -12.165525061.Subproblem 1
w + 2 = 12.165525061 Simplifying w + 2 = 12.165525061 Reorder the terms: 2 + w = 12.165525061 Solving 2 + w = 12.165525061 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 12.165525061 + -2 Combine like terms: 2 + -2 = 0 0 + w = 12.165525061 + -2 w = 12.165525061 + -2 Combine like terms: 12.165525061 + -2 = 10.165525061 w = 10.165525061 Simplifying w = 10.165525061Subproblem 2
w + 2 = -12.165525061 Simplifying w + 2 = -12.165525061 Reorder the terms: 2 + w = -12.165525061 Solving 2 + w = -12.165525061 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -12.165525061 + -2 Combine like terms: 2 + -2 = 0 0 + w = -12.165525061 + -2 w = -12.165525061 + -2 Combine like terms: -12.165525061 + -2 = -14.165525061 w = -14.165525061 Simplifying w = -14.165525061Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.165525061, -14.165525061}
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