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Simplifying -2w2 + -9w + 4 = 0 Reorder the terms: 4 + -9w + -2w2 = 0 Solving 4 + -9w + -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'. -2 + 4.5w + w2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 4.5w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + 4.5w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4.5w + w2 = 0 + 2 4.5w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 4.5w + w2 = 2 The w term is 4.5w. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5w + 5.0625 + w2 = 2 + 5.0625 Reorder the terms: 5.0625 + 4.5w + w2 = 2 + 5.0625 Combine like terms: 2 + 5.0625 = 7.0625 5.0625 + 4.5w + w2 = 7.0625 Factor a perfect square on the left side: (w + 2.25)(w + 2.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (w + 2.25) equal to 2.657536453 and -2.657536453.Subproblem 1
w + 2.25 = 2.657536453 Simplifying w + 2.25 = 2.657536453 Reorder the terms: 2.25 + w = 2.657536453 Solving 2.25 + w = 2.657536453 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + w = 2.657536453 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + w = 2.657536453 + -2.25 w = 2.657536453 + -2.25 Combine like terms: 2.657536453 + -2.25 = 0.407536453 w = 0.407536453 Simplifying w = 0.407536453Subproblem 2
w + 2.25 = -2.657536453 Simplifying w + 2.25 = -2.657536453 Reorder the terms: 2.25 + w = -2.657536453 Solving 2.25 + w = -2.657536453 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + w = -2.657536453 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + w = -2.657536453 + -2.25 w = -2.657536453 + -2.25 Combine like terms: -2.657536453 + -2.25 = -4.907536453 w = -4.907536453 Simplifying w = -4.907536453Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.407536453, -4.907536453}
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