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Simplifying 0 = w2 + -6w + -80 Reorder the terms: 0 = -80 + -6w + w2 Solving 0 = -80 + -6w + w2 Solving for variable 'w'. Combine like terms: 0 + 80 = 80 80 + 6w + -1w2 = -80 + -6w + w2 + 80 + 6w + -1w2 Reorder the terms: 80 + 6w + -1w2 = -80 + 80 + -6w + 6w + w2 + -1w2 Combine like terms: -80 + 80 = 0 80 + 6w + -1w2 = 0 + -6w + 6w + w2 + -1w2 80 + 6w + -1w2 = -6w + 6w + w2 + -1w2 Combine like terms: -6w + 6w = 0 80 + 6w + -1w2 = 0 + w2 + -1w2 80 + 6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 80 + 6w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + -6w + w2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -6w + 80 + w2 = 0 + 80 Reorder the terms: -80 + 80 + -6w + w2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -6w + w2 = 0 + 80 -6w + w2 = 0 + 80 Combine like terms: 0 + 80 = 80 -6w + w2 = 80 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 = 80 + 9 Reorder the terms: 9 + -6w + w2 = 80 + 9 Combine like terms: 80 + 9 = 89 9 + -6w + w2 = 89 Factor a perfect square on the left side: (w + -3)(w + -3) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (w + -3) equal to 9.433981132 and -9.433981132.Subproblem 1
w + -3 = 9.433981132 Simplifying w + -3 = 9.433981132 Reorder the terms: -3 + w = 9.433981132 Solving -3 + w = 9.433981132 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 = 9.433981132 + 3 Combine like terms: -3 + 3 = 0 0 + w = 9.433981132 + 3 w = 9.433981132 + 3 Combine like terms: 9.433981132 + 3 = 12.433981132 w = 12.433981132 Simplifying w = 12.433981132Subproblem 2
w + -3 = -9.433981132 Simplifying w + -3 = -9.433981132 Reorder the terms: -3 + w = -9.433981132 Solving -3 + w = -9.433981132 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 = -9.433981132 + 3 Combine like terms: -3 + 3 = 0 0 + w = -9.433981132 + 3 w = -9.433981132 + 3 Combine like terms: -9.433981132 + 3 = -6.433981132 w = -6.433981132 Simplifying w = -6.433981132Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.433981132, -6.433981132}
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