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Simplifying w2 + -15w + 1 = 0 Reorder the terms: 1 + -15w + w2 = 0 Solving 1 + -15w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -15w + -1 + w2 = 0 + -1 Reorder the terms: 1 + -1 + -15w + w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -15w + w2 = 0 + -1 -15w + w2 = 0 + -1 Combine like terms: 0 + -1 = -1 -15w + w2 = -1 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 = -1 + 56.25 Reorder the terms: 56.25 + -15w + w2 = -1 + 56.25 Combine like terms: -1 + 56.25 = 55.25 56.25 + -15w + w2 = 55.25 Factor a perfect square on the left side: (w + -7.5)(w + -7.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (w + -7.5) equal to 7.433034374 and -7.433034374.Subproblem 1
w + -7.5 = 7.433034374 Simplifying w + -7.5 = 7.433034374 Reorder the terms: -7.5 + w = 7.433034374 Solving -7.5 + w = 7.433034374 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 = 7.433034374 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + w = 7.433034374 + 7.5 w = 7.433034374 + 7.5 Combine like terms: 7.433034374 + 7.5 = 14.933034374 w = 14.933034374 Simplifying w = 14.933034374Subproblem 2
w + -7.5 = -7.433034374 Simplifying w + -7.5 = -7.433034374 Reorder the terms: -7.5 + w = -7.433034374 Solving -7.5 + w = -7.433034374 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 = -7.433034374 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + w = -7.433034374 + 7.5 w = -7.433034374 + 7.5 Combine like terms: -7.433034374 + 7.5 = 0.066965626 w = 0.066965626 Simplifying w = 0.066965626Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.933034374, 0.066965626}
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