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Simplifying 2w2 + 14w + 3 = 0 Reorder the terms: 3 + 14w + 2w2 = 0 Solving 3 + 14w + 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'. 1.5 + 7w + w2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 7w + -1.5 + w2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 7w + w2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 7w + w2 = 0 + -1.5 7w + w2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 7w + w2 = -1.5 The w term is 7w. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7w + 12.25 + w2 = -1.5 + 12.25 Reorder the terms: 12.25 + 7w + w2 = -1.5 + 12.25 Combine like terms: -1.5 + 12.25 = 10.75 12.25 + 7w + w2 = 10.75 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (w + 3.5) equal to 3.278719262 and -3.278719262.Subproblem 1
w + 3.5 = 3.278719262 Simplifying w + 3.5 = 3.278719262 Reorder the terms: 3.5 + w = 3.278719262 Solving 3.5 + w = 3.278719262 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = 3.278719262 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 3.278719262 + -3.5 w = 3.278719262 + -3.5 Combine like terms: 3.278719262 + -3.5 = -0.221280738 w = -0.221280738 Simplifying w = -0.221280738Subproblem 2
w + 3.5 = -3.278719262 Simplifying w + 3.5 = -3.278719262 Reorder the terms: 3.5 + w = -3.278719262 Solving 3.5 + w = -3.278719262 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = -3.278719262 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -3.278719262 + -3.5 w = -3.278719262 + -3.5 Combine like terms: -3.278719262 + -3.5 = -6.778719262 w = -6.778719262 Simplifying w = -6.778719262Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.221280738, -6.778719262}
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