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Simplifying -4w2 + 14w + 9 = 0 Reorder the terms: 9 + 14w + -4w2 = 0 Solving 9 + 14w + -4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.25 + -3.5w + w2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -3.5w + 2.25 + w2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -3.5w + w2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -3.5w + w2 = 0 + 2.25 -3.5w + w2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -3.5w + w2 = 2.25 The w term is -3.5w. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5w + 3.0625 + w2 = 2.25 + 3.0625 Reorder the terms: 3.0625 + -3.5w + w2 = 2.25 + 3.0625 Combine like terms: 2.25 + 3.0625 = 5.3125 3.0625 + -3.5w + w2 = 5.3125 Factor a perfect square on the left side: (w + -1.75)(w + -1.75) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (w + -1.75) equal to 2.304886114 and -2.304886114.Subproblem 1
w + -1.75 = 2.304886114 Simplifying w + -1.75 = 2.304886114 Reorder the terms: -1.75 + w = 2.304886114 Solving -1.75 + w = 2.304886114 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = 2.304886114 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = 2.304886114 + 1.75 w = 2.304886114 + 1.75 Combine like terms: 2.304886114 + 1.75 = 4.054886114 w = 4.054886114 Simplifying w = 4.054886114Subproblem 2
w + -1.75 = -2.304886114 Simplifying w + -1.75 = -2.304886114 Reorder the terms: -1.75 + w = -2.304886114 Solving -1.75 + w = -2.304886114 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = -2.304886114 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = -2.304886114 + 1.75 w = -2.304886114 + 1.75 Combine like terms: -2.304886114 + 1.75 = -0.554886114 w = -0.554886114 Simplifying w = -0.554886114Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.054886114, -0.554886114}
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