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Simplifying w2 + 20w + 72 = 320 Reorder the terms: 72 + 20w + w2 = 320 Solving 72 + 20w + w2 = 320 Solving for variable 'w'. Reorder the terms: 72 + -320 + 20w + w2 = 320 + -320 Combine like terms: 72 + -320 = -248 -248 + 20w + w2 = 320 + -320 Combine like terms: 320 + -320 = 0 -248 + 20w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '248' to each side of the equation. -248 + 20w + 248 + w2 = 0 + 248 Reorder the terms: -248 + 248 + 20w + w2 = 0 + 248 Combine like terms: -248 + 248 = 0 0 + 20w + w2 = 0 + 248 20w + w2 = 0 + 248 Combine like terms: 0 + 248 = 248 20w + w2 = 248 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 = 248 + 100 Reorder the terms: 100 + 20w + w2 = 248 + 100 Combine like terms: 248 + 100 = 348 100 + 20w + w2 = 348 Factor a perfect square on the left side: (w + 10)(w + 10) = 348 Calculate the square root of the right side: 18.654758106 Break this problem into two subproblems by setting (w + 10) equal to 18.654758106 and -18.654758106.Subproblem 1
w + 10 = 18.654758106 Simplifying w + 10 = 18.654758106 Reorder the terms: 10 + w = 18.654758106 Solving 10 + w = 18.654758106 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 = 18.654758106 + -10 Combine like terms: 10 + -10 = 0 0 + w = 18.654758106 + -10 w = 18.654758106 + -10 Combine like terms: 18.654758106 + -10 = 8.654758106 w = 8.654758106 Simplifying w = 8.654758106Subproblem 2
w + 10 = -18.654758106 Simplifying w + 10 = -18.654758106 Reorder the terms: 10 + w = -18.654758106 Solving 10 + w = -18.654758106 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 = -18.654758106 + -10 Combine like terms: 10 + -10 = 0 0 + w = -18.654758106 + -10 w = -18.654758106 + -10 Combine like terms: -18.654758106 + -10 = -28.654758106 w = -28.654758106 Simplifying w = -28.654758106Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.654758106, -28.654758106}
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