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Simplifying w2 + 10w + -360 = 0 Reorder the terms: -360 + 10w + w2 = 0 Solving -360 + 10w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 10w + 360 + w2 = 0 + 360 Reorder the terms: -360 + 360 + 10w + w2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 10w + w2 = 0 + 360 10w + w2 = 0 + 360 Combine like terms: 0 + 360 = 360 10w + w2 = 360 The w term is 10w. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10w + 25 + w2 = 360 + 25 Reorder the terms: 25 + 10w + w2 = 360 + 25 Combine like terms: 360 + 25 = 385 25 + 10w + w2 = 385 Factor a perfect square on the left side: (w + 5)(w + 5) = 385 Calculate the square root of the right side: 19.62141687 Break this problem into two subproblems by setting (w + 5) equal to 19.62141687 and -19.62141687.Subproblem 1
w + 5 = 19.62141687 Simplifying w + 5 = 19.62141687 Reorder the terms: 5 + w = 19.62141687 Solving 5 + w = 19.62141687 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 19.62141687 + -5 Combine like terms: 5 + -5 = 0 0 + w = 19.62141687 + -5 w = 19.62141687 + -5 Combine like terms: 19.62141687 + -5 = 14.62141687 w = 14.62141687 Simplifying w = 14.62141687Subproblem 2
w + 5 = -19.62141687 Simplifying w + 5 = -19.62141687 Reorder the terms: 5 + w = -19.62141687 Solving 5 + w = -19.62141687 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = -19.62141687 + -5 Combine like terms: 5 + -5 = 0 0 + w = -19.62141687 + -5 w = -19.62141687 + -5 Combine like terms: -19.62141687 + -5 = -24.62141687 w = -24.62141687 Simplifying w = -24.62141687Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.62141687, -24.62141687}
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