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Simplifying w2 = 2w + 21 Reorder the terms: w2 = 21 + 2w Solving w2 = 21 + 2w Solving for variable 'w'. Reorder the terms: -21 + -2w + w2 = 21 + 2w + -21 + -2w Reorder the terms: -21 + -2w + w2 = 21 + -21 + 2w + -2w Combine like terms: 21 + -21 = 0 -21 + -2w + w2 = 0 + 2w + -2w -21 + -2w + w2 = 2w + -2w Combine like terms: 2w + -2w = 0 -21 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -2w + 21 + w2 = 0 + 21 Reorder the terms: -21 + 21 + -2w + w2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2w + w2 = 0 + 21 -2w + w2 = 0 + 21 Combine like terms: 0 + 21 = 21 -2w + w2 = 21 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 = 21 + 1 Reorder the terms: 1 + -2w + w2 = 21 + 1 Combine like terms: 21 + 1 = 22 1 + -2w + w2 = 22 Factor a perfect square on the left side: (w + -1)(w + -1) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (w + -1) equal to 4.69041576 and -4.69041576.Subproblem 1
w + -1 = 4.69041576 Simplifying w + -1 = 4.69041576 Reorder the terms: -1 + w = 4.69041576 Solving -1 + w = 4.69041576 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 = 4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + w = 4.69041576 + 1 w = 4.69041576 + 1 Combine like terms: 4.69041576 + 1 = 5.69041576 w = 5.69041576 Simplifying w = 5.69041576Subproblem 2
w + -1 = -4.69041576 Simplifying w + -1 = -4.69041576 Reorder the terms: -1 + w = -4.69041576 Solving -1 + w = -4.69041576 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 = -4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + w = -4.69041576 + 1 w = -4.69041576 + 1 Combine like terms: -4.69041576 + 1 = -3.69041576 w = -3.69041576 Simplifying w = -3.69041576Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.69041576, -3.69041576}
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