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Simplifying w2 + 22w = -25 Reorder the terms: 22w + w2 = -25 Solving 22w + w2 = -25 Solving for variable 'w'. Reorder the terms: 25 + 22w + w2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + 22w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 22w + -25 + w2 = 0 + -25 Reorder the terms: 25 + -25 + 22w + w2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 22w + w2 = 0 + -25 22w + w2 = 0 + -25 Combine like terms: 0 + -25 = -25 22w + w2 = -25 The w term is 22w. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22w + 121 + w2 = -25 + 121 Reorder the terms: 121 + 22w + w2 = -25 + 121 Combine like terms: -25 + 121 = 96 121 + 22w + w2 = 96 Factor a perfect square on the left side: (w + 11)(w + 11) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (w + 11) equal to 9.797958971 and -9.797958971.Subproblem 1
w + 11 = 9.797958971 Simplifying w + 11 = 9.797958971 Reorder the terms: 11 + w = 9.797958971 Solving 11 + w = 9.797958971 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + w = 9.797958971 + -11 Combine like terms: 11 + -11 = 0 0 + w = 9.797958971 + -11 w = 9.797958971 + -11 Combine like terms: 9.797958971 + -11 = -1.202041029 w = -1.202041029 Simplifying w = -1.202041029Subproblem 2
w + 11 = -9.797958971 Simplifying w + 11 = -9.797958971 Reorder the terms: 11 + w = -9.797958971 Solving 11 + w = -9.797958971 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + w = -9.797958971 + -11 Combine like terms: 11 + -11 = 0 0 + w = -9.797958971 + -11 w = -9.797958971 + -11 Combine like terms: -9.797958971 + -11 = -20.797958971 w = -20.797958971 Simplifying w = -20.797958971Solution
The solution to the problem is based on the solutions from the subproblems. w = {-1.202041029, -20.797958971}
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