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Simplifying w2 = 6 + 2w Solving w2 = 6 + 2w Solving for variable 'w'. Reorder the terms: -6 + -2w + w2 = 6 + 2w + -6 + -2w Reorder the terms: -6 + -2w + w2 = 6 + -6 + 2w + -2w Combine like terms: 6 + -6 = 0 -6 + -2w + w2 = 0 + 2w + -2w -6 + -2w + w2 = 2w + -2w Combine like terms: 2w + -2w = 0 -6 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -2w + 6 + w2 = 0 + 6 Reorder the terms: -6 + 6 + -2w + w2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2w + w2 = 0 + 6 -2w + w2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2w + w2 = 6 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 6 + 1 Reorder the terms: 1 + -2w + w2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2w + w2 = 7 Factor a perfect square on the left side: (w + -1)(w + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (w + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
w + -1 = 2.645751311 Simplifying w + -1 = 2.645751311 Reorder the terms: -1 + w = 2.645751311 Solving -1 + w = 2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + w = 2.645751311 + 1 w = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 w = 3.645751311 Simplifying w = 3.645751311Subproblem 2
w + -1 = -2.645751311 Simplifying w + -1 = -2.645751311 Reorder the terms: -1 + w = -2.645751311 Solving -1 + w = -2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + w = -2.645751311 + 1 w = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 w = -1.645751311 Simplifying w = -1.645751311Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.645751311, -1.645751311}
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