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Simplifying w2 + 6w = 84 Reorder the terms: 6w + w2 = 84 Solving 6w + w2 = 84 Solving for variable 'w'. Reorder the terms: -84 + 6w + w2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 6w + 84 + w2 = 0 + 84 Reorder the terms: -84 + 84 + 6w + w2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 6w + w2 = 0 + 84 6w + w2 = 0 + 84 Combine like terms: 0 + 84 = 84 6w + w2 = 84 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 = 84 + 9 Reorder the terms: 9 + 6w + w2 = 84 + 9 Combine like terms: 84 + 9 = 93 9 + 6w + w2 = 93 Factor a perfect square on the left side: (w + 3)(w + 3) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (w + 3) equal to 9.643650761 and -9.643650761.Subproblem 1
w + 3 = 9.643650761 Simplifying w + 3 = 9.643650761 Reorder the terms: 3 + w = 9.643650761 Solving 3 + w = 9.643650761 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 = 9.643650761 + -3 Combine like terms: 3 + -3 = 0 0 + w = 9.643650761 + -3 w = 9.643650761 + -3 Combine like terms: 9.643650761 + -3 = 6.643650761 w = 6.643650761 Simplifying w = 6.643650761Subproblem 2
w + 3 = -9.643650761 Simplifying w + 3 = -9.643650761 Reorder the terms: 3 + w = -9.643650761 Solving 3 + w = -9.643650761 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 = -9.643650761 + -3 Combine like terms: 3 + -3 = 0 0 + w = -9.643650761 + -3 w = -9.643650761 + -3 Combine like terms: -9.643650761 + -3 = -12.643650761 w = -12.643650761 Simplifying w = -12.643650761Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.643650761, -12.643650761}
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