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Simplifying w2 + -8w + 9 = 0 Reorder the terms: 9 + -8w + w2 = 0 Solving 9 + -8w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8w + -9 + w2 = 0 + -9 Reorder the terms: 9 + -9 + -8w + w2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8w + w2 = 0 + -9 -8w + w2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8w + w2 = -9 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 = -9 + 16 Reorder the terms: 16 + -8w + w2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + -8w + w2 = 7 Factor a perfect square on the left side: (w + -4)(w + -4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (w + -4) equal to 2.645751311 and -2.645751311.Subproblem 1
w + -4 = 2.645751311 Simplifying w + -4 = 2.645751311 Reorder the terms: -4 + w = 2.645751311 Solving -4 + w = 2.645751311 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 = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + w = 2.645751311 + 4 w = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 w = 6.645751311 Simplifying w = 6.645751311Subproblem 2
w + -4 = -2.645751311 Simplifying w + -4 = -2.645751311 Reorder the terms: -4 + w = -2.645751311 Solving -4 + w = -2.645751311 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 = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + w = -2.645751311 + 4 w = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 w = 1.354248689 Simplifying w = 1.354248689Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.645751311, 1.354248689}
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