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Simplifying -9w2 + -4w + 2 = 0 Reorder the terms: 2 + -4w + -9w2 = 0 Solving 2 + -4w + -9w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.2222222222 + 0.4444444444w + w2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.4444444444w + 0.2222222222 + w2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 0.4444444444w + w2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 0.4444444444w + w2 = 0 + 0.2222222222 0.4444444444w + w2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 0.4444444444w + w2 = 0.2222222222 The w term is 0.4444444444w. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444w + 0.04938271604 + w2 = 0.2222222222 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444w + w2 = 0.2222222222 + 0.04938271604 Combine like terms: 0.2222222222 + 0.04938271604 = 0.27160493824 0.04938271604 + 0.4444444444w + w2 = 0.27160493824 Factor a perfect square on the left side: (w + 0.2222222222)(w + 0.2222222222) = 0.27160493824 Calculate the square root of the right side: 0.521157307 Break this problem into two subproblems by setting (w + 0.2222222222) equal to 0.521157307 and -0.521157307.Subproblem 1
w + 0.2222222222 = 0.521157307 Simplifying w + 0.2222222222 = 0.521157307 Reorder the terms: 0.2222222222 + w = 0.521157307 Solving 0.2222222222 + w = 0.521157307 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + w = 0.521157307 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + w = 0.521157307 + -0.2222222222 w = 0.521157307 + -0.2222222222 Combine like terms: 0.521157307 + -0.2222222222 = 0.2989350848 w = 0.2989350848 Simplifying w = 0.2989350848Subproblem 2
w + 0.2222222222 = -0.521157307 Simplifying w + 0.2222222222 = -0.521157307 Reorder the terms: 0.2222222222 + w = -0.521157307 Solving 0.2222222222 + w = -0.521157307 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + w = -0.521157307 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + w = -0.521157307 + -0.2222222222 w = -0.521157307 + -0.2222222222 Combine like terms: -0.521157307 + -0.2222222222 = -0.7433795292 w = -0.7433795292 Simplifying w = -0.7433795292Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.2989350848, -0.7433795292}
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