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Simplifying w2 + 15w + -48 = 0 Reorder the terms: -48 + 15w + w2 = 0 Solving -48 + 15w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 15w + 48 + w2 = 0 + 48 Reorder the terms: -48 + 48 + 15w + w2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 15w + w2 = 0 + 48 15w + w2 = 0 + 48 Combine like terms: 0 + 48 = 48 15w + w2 = 48 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 = 48 + 56.25 Reorder the terms: 56.25 + 15w + w2 = 48 + 56.25 Combine like terms: 48 + 56.25 = 104.25 56.25 + 15w + w2 = 104.25 Factor a perfect square on the left side: (w + 7.5)(w + 7.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (w + 7.5) equal to 10.210288928 and -10.210288928.Subproblem 1
w + 7.5 = 10.210288928 Simplifying w + 7.5 = 10.210288928 Reorder the terms: 7.5 + w = 10.210288928 Solving 7.5 + w = 10.210288928 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 = 10.210288928 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 10.210288928 + -7.5 w = 10.210288928 + -7.5 Combine like terms: 10.210288928 + -7.5 = 2.710288928 w = 2.710288928 Simplifying w = 2.710288928Subproblem 2
w + 7.5 = -10.210288928 Simplifying w + 7.5 = -10.210288928 Reorder the terms: 7.5 + w = -10.210288928 Solving 7.5 + w = -10.210288928 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 = -10.210288928 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -10.210288928 + -7.5 w = -10.210288928 + -7.5 Combine like terms: -10.210288928 + -7.5 = -17.710288928 w = -17.710288928 Simplifying w = -17.710288928Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.710288928, -17.710288928}
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