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Simplifying w2 + 20w + 50 = 0 Reorder the terms: 50 + 20w + w2 = 0 Solving 50 + 20w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + 20w + -50 + w2 = 0 + -50 Reorder the terms: 50 + -50 + 20w + w2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 20w + w2 = 0 + -50 20w + w2 = 0 + -50 Combine like terms: 0 + -50 = -50 20w + w2 = -50 The w term is 20w. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20w + 100 + w2 = -50 + 100 Reorder the terms: 100 + 20w + w2 = -50 + 100 Combine like terms: -50 + 100 = 50 100 + 20w + w2 = 50 Factor a perfect square on the left side: (w + 10)(w + 10) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (w + 10) equal to 7.071067812 and -7.071067812.Subproblem 1
w + 10 = 7.071067812 Simplifying w + 10 = 7.071067812 Reorder the terms: 10 + w = 7.071067812 Solving 10 + w = 7.071067812 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = 7.071067812 + -10 Combine like terms: 10 + -10 = 0 0 + w = 7.071067812 + -10 w = 7.071067812 + -10 Combine like terms: 7.071067812 + -10 = -2.928932188 w = -2.928932188 Simplifying w = -2.928932188Subproblem 2
w + 10 = -7.071067812 Simplifying w + 10 = -7.071067812 Reorder the terms: 10 + w = -7.071067812 Solving 10 + w = -7.071067812 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = -7.071067812 + -10 Combine like terms: 10 + -10 = 0 0 + w = -7.071067812 + -10 w = -7.071067812 + -10 Combine like terms: -7.071067812 + -10 = -17.071067812 w = -17.071067812 Simplifying w = -17.071067812Solution
The solution to the problem is based on the solutions from the subproblems. w = {-2.928932188, -17.071067812}
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