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Simplifying 5w2 + -4w + -440 = 0 Reorder the terms: -440 + -4w + 5w2 = 0 Solving -440 + -4w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -88 + -0.8w + w2 = 0 Move the constant term to the right: Add '88' to each side of the equation. -88 + -0.8w + 88 + w2 = 0 + 88 Reorder the terms: -88 + 88 + -0.8w + w2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -0.8w + w2 = 0 + 88 -0.8w + w2 = 0 + 88 Combine like terms: 0 + 88 = 88 -0.8w + w2 = 88 The w term is -0.8w. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8w + 0.16 + w2 = 88 + 0.16 Reorder the terms: 0.16 + -0.8w + w2 = 88 + 0.16 Combine like terms: 88 + 0.16 = 88.16 0.16 + -0.8w + w2 = 88.16 Factor a perfect square on the left side: (w + -0.4)(w + -0.4) = 88.16 Calculate the square root of the right side: 9.389355675 Break this problem into two subproblems by setting (w + -0.4) equal to 9.389355675 and -9.389355675.Subproblem 1
w + -0.4 = 9.389355675 Simplifying w + -0.4 = 9.389355675 Reorder the terms: -0.4 + w = 9.389355675 Solving -0.4 + w = 9.389355675 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + w = 9.389355675 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + w = 9.389355675 + 0.4 w = 9.389355675 + 0.4 Combine like terms: 9.389355675 + 0.4 = 9.789355675 w = 9.789355675 Simplifying w = 9.789355675Subproblem 2
w + -0.4 = -9.389355675 Simplifying w + -0.4 = -9.389355675 Reorder the terms: -0.4 + w = -9.389355675 Solving -0.4 + w = -9.389355675 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + w = -9.389355675 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + w = -9.389355675 + 0.4 w = -9.389355675 + 0.4 Combine like terms: -9.389355675 + 0.4 = -8.989355675 w = -8.989355675 Simplifying w = -8.989355675Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.789355675, -8.989355675}
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