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Simplifying 0 = w2 + 20w + -30 Reorder the terms: 0 = -30 + 20w + w2 Solving 0 = -30 + 20w + w2 Solving for variable 'w'. Combine like terms: 0 + 30 = 30 30 + -20w + -1w2 = -30 + 20w + w2 + 30 + -20w + -1w2 Reorder the terms: 30 + -20w + -1w2 = -30 + 30 + 20w + -20w + w2 + -1w2 Combine like terms: -30 + 30 = 0 30 + -20w + -1w2 = 0 + 20w + -20w + w2 + -1w2 30 + -20w + -1w2 = 20w + -20w + w2 + -1w2 Combine like terms: 20w + -20w = 0 30 + -20w + -1w2 = 0 + w2 + -1w2 30 + -20w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 30 + -20w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 20w + w2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 20w + 30 + w2 = 0 + 30 Reorder the terms: -30 + 30 + 20w + w2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 20w + w2 = 0 + 30 20w + w2 = 0 + 30 Combine like terms: 0 + 30 = 30 20w + w2 = 30 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 = 30 + 100 Reorder the terms: 100 + 20w + w2 = 30 + 100 Combine like terms: 30 + 100 = 130 100 + 20w + w2 = 130 Factor a perfect square on the left side: (w + 10)(w + 10) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (w + 10) equal to 11.401754251 and -11.401754251.Subproblem 1
w + 10 = 11.401754251 Simplifying w + 10 = 11.401754251 Reorder the terms: 10 + w = 11.401754251 Solving 10 + w = 11.401754251 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 = 11.401754251 + -10 Combine like terms: 10 + -10 = 0 0 + w = 11.401754251 + -10 w = 11.401754251 + -10 Combine like terms: 11.401754251 + -10 = 1.401754251 w = 1.401754251 Simplifying w = 1.401754251Subproblem 2
w + 10 = -11.401754251 Simplifying w + 10 = -11.401754251 Reorder the terms: 10 + w = -11.401754251 Solving 10 + w = -11.401754251 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 = -11.401754251 + -10 Combine like terms: 10 + -10 = 0 0 + w = -11.401754251 + -10 w = -11.401754251 + -10 Combine like terms: -11.401754251 + -10 = -21.401754251 w = -21.401754251 Simplifying w = -21.401754251Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.401754251, -21.401754251}
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