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Simplifying w2 + 19w + 52 = 0 Reorder the terms: 52 + 19w + w2 = 0 Solving 52 + 19w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + 19w + -52 + w2 = 0 + -52 Reorder the terms: 52 + -52 + 19w + w2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + 19w + w2 = 0 + -52 19w + w2 = 0 + -52 Combine like terms: 0 + -52 = -52 19w + w2 = -52 The w term is 19w. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19w + 90.25 + w2 = -52 + 90.25 Reorder the terms: 90.25 + 19w + w2 = -52 + 90.25 Combine like terms: -52 + 90.25 = 38.25 90.25 + 19w + w2 = 38.25 Factor a perfect square on the left side: (w + 9.5)(w + 9.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (w + 9.5) equal to 6.184658438 and -6.184658438.Subproblem 1
w + 9.5 = 6.184658438 Simplifying w + 9.5 = 6.184658438 Reorder the terms: 9.5 + w = 6.184658438 Solving 9.5 + w = 6.184658438 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + w = 6.184658438 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + w = 6.184658438 + -9.5 w = 6.184658438 + -9.5 Combine like terms: 6.184658438 + -9.5 = -3.315341562 w = -3.315341562 Simplifying w = -3.315341562Subproblem 2
w + 9.5 = -6.184658438 Simplifying w + 9.5 = -6.184658438 Reorder the terms: 9.5 + w = -6.184658438 Solving 9.5 + w = -6.184658438 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + w = -6.184658438 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + w = -6.184658438 + -9.5 w = -6.184658438 + -9.5 Combine like terms: -6.184658438 + -9.5 = -15.684658438 w = -15.684658438 Simplifying w = -15.684658438Solution
The solution to the problem is based on the solutions from the subproblems. w = {-3.315341562, -15.684658438}
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