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Simplifying w2 + -8w + 3 = 0 Reorder the terms: 3 + -8w + w2 = 0 Solving 3 + -8w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8w + -3 + w2 = 0 + -3 Reorder the terms: 3 + -3 + -8w + w2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8w + w2 = 0 + -3 -8w + w2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8w + w2 = -3 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 = -3 + 16 Reorder the terms: 16 + -8w + w2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8w + w2 = 13 Factor a perfect square on the left side: (w + -4)(w + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (w + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
w + -4 = 3.605551275 Simplifying w + -4 = 3.605551275 Reorder the terms: -4 + w = 3.605551275 Solving -4 + w = 3.605551275 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 = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + w = 3.605551275 + 4 w = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 w = 7.605551275 Simplifying w = 7.605551275Subproblem 2
w + -4 = -3.605551275 Simplifying w + -4 = -3.605551275 Reorder the terms: -4 + w = -3.605551275 Solving -4 + w = -3.605551275 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 = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + w = -3.605551275 + 4 w = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 w = 0.394448725 Simplifying w = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.605551275, 0.394448725}
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