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Simplifying 2w2 + 3w + -64 = 0 Reorder the terms: -64 + 3w + 2w2 = 0 Solving -64 + 3w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -32 + 1.5w + w2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 1.5w + 32 + w2 = 0 + 32 Reorder the terms: -32 + 32 + 1.5w + w2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 1.5w + w2 = 0 + 32 1.5w + w2 = 0 + 32 Combine like terms: 0 + 32 = 32 1.5w + w2 = 32 The w term is 1.5w. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5w + 0.5625 + w2 = 32 + 0.5625 Reorder the terms: 0.5625 + 1.5w + w2 = 32 + 0.5625 Combine like terms: 32 + 0.5625 = 32.5625 0.5625 + 1.5w + w2 = 32.5625 Factor a perfect square on the left side: (w + 0.75)(w + 0.75) = 32.5625 Calculate the square root of the right side: 5.706356105 Break this problem into two subproblems by setting (w + 0.75) equal to 5.706356105 and -5.706356105.Subproblem 1
w + 0.75 = 5.706356105 Simplifying w + 0.75 = 5.706356105 Reorder the terms: 0.75 + w = 5.706356105 Solving 0.75 + w = 5.706356105 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + w = 5.706356105 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + w = 5.706356105 + -0.75 w = 5.706356105 + -0.75 Combine like terms: 5.706356105 + -0.75 = 4.956356105 w = 4.956356105 Simplifying w = 4.956356105Subproblem 2
w + 0.75 = -5.706356105 Simplifying w + 0.75 = -5.706356105 Reorder the terms: 0.75 + w = -5.706356105 Solving 0.75 + w = -5.706356105 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + w = -5.706356105 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + w = -5.706356105 + -0.75 w = -5.706356105 + -0.75 Combine like terms: -5.706356105 + -0.75 = -6.456356105 w = -6.456356105 Simplifying w = -6.456356105Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.956356105, -6.456356105}
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