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Simplifying 500 = w(w + 20) Reorder the terms: 500 = w(20 + w) 500 = (20 * w + w * w) 500 = (20w + w2) Solving 500 = 20w + w2 Solving for variable 'w'. Reorder the terms: 500 + -20w + -1w2 = 20w + -20w + w2 + -1w2 Combine like terms: 20w + -20w = 0 500 + -20w + -1w2 = 0 + w2 + -1w2 500 + -20w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 500 + -20w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -500 + 20w + w2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + 20w + 500 + w2 = 0 + 500 Reorder the terms: -500 + 500 + 20w + w2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 20w + w2 = 0 + 500 20w + w2 = 0 + 500 Combine like terms: 0 + 500 = 500 20w + w2 = 500 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 = 500 + 100 Reorder the terms: 100 + 20w + w2 = 500 + 100 Combine like terms: 500 + 100 = 600 100 + 20w + w2 = 600 Factor a perfect square on the left side: (w + 10)(w + 10) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (w + 10) equal to 24.494897428 and -24.494897428.Subproblem 1
w + 10 = 24.494897428 Simplifying w + 10 = 24.494897428 Reorder the terms: 10 + w = 24.494897428 Solving 10 + w = 24.494897428 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 = 24.494897428 + -10 Combine like terms: 10 + -10 = 0 0 + w = 24.494897428 + -10 w = 24.494897428 + -10 Combine like terms: 24.494897428 + -10 = 14.494897428 w = 14.494897428 Simplifying w = 14.494897428Subproblem 2
w + 10 = -24.494897428 Simplifying w + 10 = -24.494897428 Reorder the terms: 10 + w = -24.494897428 Solving 10 + w = -24.494897428 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 = -24.494897428 + -10 Combine like terms: 10 + -10 = 0 0 + w = -24.494897428 + -10 w = -24.494897428 + -10 Combine like terms: -24.494897428 + -10 = -34.494897428 w = -34.494897428 Simplifying w = -34.494897428Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.494897428, -34.494897428}
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