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Simplifying w2 + -8w + 1 = 0 Reorder the terms: 1 + -8w + w2 = 0 Solving 1 + -8w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8w + -1 + w2 = 0 + -1 Reorder the terms: 1 + -1 + -8w + w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8w + w2 = 0 + -1 -8w + w2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8w + w2 = -1 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 = -1 + 16 Reorder the terms: 16 + -8w + w2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + -8w + w2 = 15 Factor a perfect square on the left side: (w + -4)(w + -4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (w + -4) equal to 3.872983346 and -3.872983346.Subproblem 1
w + -4 = 3.872983346 Simplifying w + -4 = 3.872983346 Reorder the terms: -4 + w = 3.872983346 Solving -4 + w = 3.872983346 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 = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + w = 3.872983346 + 4 w = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 w = 7.872983346 Simplifying w = 7.872983346Subproblem 2
w + -4 = -3.872983346 Simplifying w + -4 = -3.872983346 Reorder the terms: -4 + w = -3.872983346 Solving -4 + w = -3.872983346 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 = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + w = -3.872983346 + 4 w = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 w = 0.127016654 Simplifying w = 0.127016654Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.872983346, 0.127016654}
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