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Simplifying w2 + -10w = 4 Reorder the terms: -10w + w2 = 4 Solving -10w + w2 = 4 Solving for variable 'w'. Reorder the terms: -4 + -10w + w2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -10w + 4 + w2 = 0 + 4 Reorder the terms: -4 + 4 + -10w + w2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -10w + w2 = 0 + 4 -10w + w2 = 0 + 4 Combine like terms: 0 + 4 = 4 -10w + w2 = 4 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 = 4 + 25 Reorder the terms: 25 + -10w + w2 = 4 + 25 Combine like terms: 4 + 25 = 29 25 + -10w + w2 = 29 Factor a perfect square on the left side: (w + -5)(w + -5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (w + -5) equal to 5.385164807 and -5.385164807.Subproblem 1
w + -5 = 5.385164807 Simplifying w + -5 = 5.385164807 Reorder the terms: -5 + w = 5.385164807 Solving -5 + w = 5.385164807 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 = 5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + w = 5.385164807 + 5 w = 5.385164807 + 5 Combine like terms: 5.385164807 + 5 = 10.385164807 w = 10.385164807 Simplifying w = 10.385164807Subproblem 2
w + -5 = -5.385164807 Simplifying w + -5 = -5.385164807 Reorder the terms: -5 + w = -5.385164807 Solving -5 + w = -5.385164807 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 = -5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + w = -5.385164807 + 5 w = -5.385164807 + 5 Combine like terms: -5.385164807 + 5 = -0.385164807 w = -0.385164807 Simplifying w = -0.385164807Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.385164807, -0.385164807}
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