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Simplifying w2 + 8w + 4 = 0 Reorder the terms: 4 + 8w + w2 = 0 Solving 4 + 8w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 8w + -4 + w2 = 0 + -4 Reorder the terms: 4 + -4 + 8w + w2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 8w + w2 = 0 + -4 8w + w2 = 0 + -4 Combine like terms: 0 + -4 = -4 8w + w2 = -4 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 = -4 + 16 Reorder the terms: 16 + 8w + w2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + 8w + w2 = 12 Factor a perfect square on the left side: (w + 4)(w + 4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (w + 4) equal to 3.464101615 and -3.464101615.Subproblem 1
w + 4 = 3.464101615 Simplifying w + 4 = 3.464101615 Reorder the terms: 4 + w = 3.464101615 Solving 4 + w = 3.464101615 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 = 3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + w = 3.464101615 + -4 w = 3.464101615 + -4 Combine like terms: 3.464101615 + -4 = -0.535898385 w = -0.535898385 Simplifying w = -0.535898385Subproblem 2
w + 4 = -3.464101615 Simplifying w + 4 = -3.464101615 Reorder the terms: 4 + w = -3.464101615 Solving 4 + w = -3.464101615 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 = -3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + w = -3.464101615 + -4 w = -3.464101615 + -4 Combine like terms: -3.464101615 + -4 = -7.464101615 w = -7.464101615 Simplifying w = -7.464101615Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.535898385, -7.464101615}
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