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Simplifying v2 + 18v = 17 Reorder the terms: 18v + v2 = 17 Solving 18v + v2 = 17 Solving for variable 'v'. Reorder the terms: -17 + 18v + v2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 18v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 18v + 17 + v2 = 0 + 17 Reorder the terms: -17 + 17 + 18v + v2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 18v + v2 = 0 + 17 18v + v2 = 0 + 17 Combine like terms: 0 + 17 = 17 18v + v2 = 17 The v term is 18v. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18v + 81 + v2 = 17 + 81 Reorder the terms: 81 + 18v + v2 = 17 + 81 Combine like terms: 17 + 81 = 98 81 + 18v + v2 = 98 Factor a perfect square on the left side: (v + 9)(v + 9) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (v + 9) equal to 9.899494937 and -9.899494937.Subproblem 1
v + 9 = 9.899494937 Simplifying v + 9 = 9.899494937 Reorder the terms: 9 + v = 9.899494937 Solving 9 + v = 9.899494937 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + v = 9.899494937 + -9 Combine like terms: 9 + -9 = 0 0 + v = 9.899494937 + -9 v = 9.899494937 + -9 Combine like terms: 9.899494937 + -9 = 0.899494937 v = 0.899494937 Simplifying v = 0.899494937Subproblem 2
v + 9 = -9.899494937 Simplifying v + 9 = -9.899494937 Reorder the terms: 9 + v = -9.899494937 Solving 9 + v = -9.899494937 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + v = -9.899494937 + -9 Combine like terms: 9 + -9 = 0 0 + v = -9.899494937 + -9 v = -9.899494937 + -9 Combine like terms: -9.899494937 + -9 = -18.899494937 v = -18.899494937 Simplifying v = -18.899494937Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.899494937, -18.899494937}
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