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Simplifying 4w2 + 40w + 1 = 0 Reorder the terms: 1 + 40w + 4w2 = 0 Solving 1 + 40w + 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'. 0.25 + 10w + w2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 10w + -0.25 + w2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 10w + w2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 10w + w2 = 0 + -0.25 10w + w2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 10w + w2 = -0.25 The w term is 10w. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10w + 25 + w2 = -0.25 + 25 Reorder the terms: 25 + 10w + w2 = -0.25 + 25 Combine like terms: -0.25 + 25 = 24.75 25 + 10w + w2 = 24.75 Factor a perfect square on the left side: (w + 5)(w + 5) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (w + 5) equal to 4.974937186 and -4.974937186.Subproblem 1
w + 5 = 4.974937186 Simplifying w + 5 = 4.974937186 Reorder the terms: 5 + w = 4.974937186 Solving 5 + w = 4.974937186 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 4.974937186 + -5 Combine like terms: 5 + -5 = 0 0 + w = 4.974937186 + -5 w = 4.974937186 + -5 Combine like terms: 4.974937186 + -5 = -0.025062814 w = -0.025062814 Simplifying w = -0.025062814Subproblem 2
w + 5 = -4.974937186 Simplifying w + 5 = -4.974937186 Reorder the terms: 5 + w = -4.974937186 Solving 5 + w = -4.974937186 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = -4.974937186 + -5 Combine like terms: 5 + -5 = 0 0 + w = -4.974937186 + -5 w = -4.974937186 + -5 Combine like terms: -4.974937186 + -5 = -9.974937186 w = -9.974937186 Simplifying w = -9.974937186Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.025062814, -9.974937186}
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