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Simplifying w2 + -6w + -64 = 0 Reorder the terms: -64 + -6w + w2 = 0 Solving -64 + -6w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -6w + 64 + w2 = 0 + 64 Reorder the terms: -64 + 64 + -6w + w2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -6w + w2 = 0 + 64 -6w + w2 = 0 + 64 Combine like terms: 0 + 64 = 64 -6w + w2 = 64 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 = 64 + 9 Reorder the terms: 9 + -6w + w2 = 64 + 9 Combine like terms: 64 + 9 = 73 9 + -6w + w2 = 73 Factor a perfect square on the left side: (w + -3)(w + -3) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (w + -3) equal to 8.544003745 and -8.544003745.Subproblem 1
w + -3 = 8.544003745 Simplifying w + -3 = 8.544003745 Reorder the terms: -3 + w = 8.544003745 Solving -3 + w = 8.544003745 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 = 8.544003745 + 3 Combine like terms: -3 + 3 = 0 0 + w = 8.544003745 + 3 w = 8.544003745 + 3 Combine like terms: 8.544003745 + 3 = 11.544003745 w = 11.544003745 Simplifying w = 11.544003745Subproblem 2
w + -3 = -8.544003745 Simplifying w + -3 = -8.544003745 Reorder the terms: -3 + w = -8.544003745 Solving -3 + w = -8.544003745 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 = -8.544003745 + 3 Combine like terms: -3 + 3 = 0 0 + w = -8.544003745 + 3 w = -8.544003745 + 3 Combine like terms: -8.544003745 + 3 = -5.544003745 w = -5.544003745 Simplifying w = -5.544003745Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.544003745, -5.544003745}
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