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Simplifying w2 + 4w = 27 Reorder the terms: 4w + w2 = 27 Solving 4w + w2 = 27 Solving for variable 'w'. Reorder the terms: -27 + 4w + w2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 4w + 27 + w2 = 0 + 27 Reorder the terms: -27 + 27 + 4w + w2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 4w + w2 = 0 + 27 4w + w2 = 0 + 27 Combine like terms: 0 + 27 = 27 4w + w2 = 27 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 = 27 + 4 Reorder the terms: 4 + 4w + w2 = 27 + 4 Combine like terms: 27 + 4 = 31 4 + 4w + w2 = 31 Factor a perfect square on the left side: (w + 2)(w + 2) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (w + 2) equal to 5.567764363 and -5.567764363.Subproblem 1
w + 2 = 5.567764363 Simplifying w + 2 = 5.567764363 Reorder the terms: 2 + w = 5.567764363 Solving 2 + w = 5.567764363 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 = 5.567764363 + -2 Combine like terms: 2 + -2 = 0 0 + w = 5.567764363 + -2 w = 5.567764363 + -2 Combine like terms: 5.567764363 + -2 = 3.567764363 w = 3.567764363 Simplifying w = 3.567764363Subproblem 2
w + 2 = -5.567764363 Simplifying w + 2 = -5.567764363 Reorder the terms: 2 + w = -5.567764363 Solving 2 + w = -5.567764363 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 = -5.567764363 + -2 Combine like terms: 2 + -2 = 0 0 + w = -5.567764363 + -2 w = -5.567764363 + -2 Combine like terms: -5.567764363 + -2 = -7.567764363 w = -7.567764363 Simplifying w = -7.567764363Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.567764363, -7.567764363}
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