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Simplifying w2 + -4 + -2w2 + -2w + 21 = 0 Reorder the terms: -4 + 21 + -2w + w2 + -2w2 = 0 Combine like terms: -4 + 21 = 17 17 + -2w + w2 + -2w2 = 0 Combine like terms: w2 + -2w2 = -1w2 17 + -2w + -1w2 = 0 Solving 17 + -2w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + 2w + w2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 2w + 17 + w2 = 0 + 17 Reorder the terms: -17 + 17 + 2w + w2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2w + w2 = 0 + 17 2w + w2 = 0 + 17 Combine like terms: 0 + 17 = 17 2w + w2 = 17 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 = 17 + 1 Reorder the terms: 1 + 2w + w2 = 17 + 1 Combine like terms: 17 + 1 = 18 1 + 2w + w2 = 18 Factor a perfect square on the left side: (w + 1)(w + 1) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (w + 1) equal to 4.242640687 and -4.242640687.Subproblem 1
w + 1 = 4.242640687 Simplifying w + 1 = 4.242640687 Reorder the terms: 1 + w = 4.242640687 Solving 1 + w = 4.242640687 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 = 4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + w = 4.242640687 + -1 w = 4.242640687 + -1 Combine like terms: 4.242640687 + -1 = 3.242640687 w = 3.242640687 Simplifying w = 3.242640687Subproblem 2
w + 1 = -4.242640687 Simplifying w + 1 = -4.242640687 Reorder the terms: 1 + w = -4.242640687 Solving 1 + w = -4.242640687 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 = -4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + w = -4.242640687 + -1 w = -4.242640687 + -1 Combine like terms: -4.242640687 + -1 = -5.242640687 w = -5.242640687 Simplifying w = -5.242640687Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.242640687, -5.242640687}
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