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Simplifying w2 + 15w + -47 = 0 Reorder the terms: -47 + 15w + w2 = 0 Solving -47 + 15w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 15w + 47 + w2 = 0 + 47 Reorder the terms: -47 + 47 + 15w + w2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 15w + w2 = 0 + 47 15w + w2 = 0 + 47 Combine like terms: 0 + 47 = 47 15w + w2 = 47 The w term is 15w. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15w + 56.25 + w2 = 47 + 56.25 Reorder the terms: 56.25 + 15w + w2 = 47 + 56.25 Combine like terms: 47 + 56.25 = 103.25 56.25 + 15w + w2 = 103.25 Factor a perfect square on the left side: (w + 7.5)(w + 7.5) = 103.25 Calculate the square root of the right side: 10.161200716 Break this problem into two subproblems by setting (w + 7.5) equal to 10.161200716 and -10.161200716.Subproblem 1
w + 7.5 = 10.161200716 Simplifying w + 7.5 = 10.161200716 Reorder the terms: 7.5 + w = 10.161200716 Solving 7.5 + w = 10.161200716 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = 10.161200716 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 10.161200716 + -7.5 w = 10.161200716 + -7.5 Combine like terms: 10.161200716 + -7.5 = 2.661200716 w = 2.661200716 Simplifying w = 2.661200716Subproblem 2
w + 7.5 = -10.161200716 Simplifying w + 7.5 = -10.161200716 Reorder the terms: 7.5 + w = -10.161200716 Solving 7.5 + w = -10.161200716 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = -10.161200716 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -10.161200716 + -7.5 w = -10.161200716 + -7.5 Combine like terms: -10.161200716 + -7.5 = -17.661200716 w = -17.661200716 Simplifying w = -17.661200716Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.661200716, -17.661200716}
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