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Simplifying w2 + 6w + -8281 = 0 Reorder the terms: -8281 + 6w + w2 = 0 Solving -8281 + 6w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '8281' to each side of the equation. -8281 + 6w + 8281 + w2 = 0 + 8281 Reorder the terms: -8281 + 8281 + 6w + w2 = 0 + 8281 Combine like terms: -8281 + 8281 = 0 0 + 6w + w2 = 0 + 8281 6w + w2 = 0 + 8281 Combine like terms: 0 + 8281 = 8281 6w + w2 = 8281 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 8281 + 9 Reorder the terms: 9 + 6w + w2 = 8281 + 9 Combine like terms: 8281 + 9 = 8290 9 + 6w + w2 = 8290 Factor a perfect square on the left side: (w + 3)(w + 3) = 8290 Calculate the square root of the right side: 91.049437121 Break this problem into two subproblems by setting (w + 3) equal to 91.049437121 and -91.049437121.Subproblem 1
w + 3 = 91.049437121 Simplifying w + 3 = 91.049437121 Reorder the terms: 3 + w = 91.049437121 Solving 3 + w = 91.049437121 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 91.049437121 + -3 Combine like terms: 3 + -3 = 0 0 + w = 91.049437121 + -3 w = 91.049437121 + -3 Combine like terms: 91.049437121 + -3 = 88.049437121 w = 88.049437121 Simplifying w = 88.049437121Subproblem 2
w + 3 = -91.049437121 Simplifying w + 3 = -91.049437121 Reorder the terms: 3 + w = -91.049437121 Solving 3 + w = -91.049437121 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -91.049437121 + -3 Combine like terms: 3 + -3 = 0 0 + w = -91.049437121 + -3 w = -91.049437121 + -3 Combine like terms: -91.049437121 + -3 = -94.049437121 w = -94.049437121 Simplifying w = -94.049437121Solution
The solution to the problem is based on the solutions from the subproblems. w = {88.049437121, -94.049437121}
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