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Simplifying v2 + -18v + 47 = 0 Reorder the terms: 47 + -18v + v2 = 0 Solving 47 + -18v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -18v + -47 + v2 = 0 + -47 Reorder the terms: 47 + -47 + -18v + v2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -18v + v2 = 0 + -47 -18v + v2 = 0 + -47 Combine like terms: 0 + -47 = -47 -18v + v2 = -47 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 = -47 + 81 Reorder the terms: 81 + -18v + v2 = -47 + 81 Combine like terms: -47 + 81 = 34 81 + -18v + v2 = 34 Factor a perfect square on the left side: (v + -9)(v + -9) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (v + -9) equal to 5.830951895 and -5.830951895.Subproblem 1
v + -9 = 5.830951895 Simplifying v + -9 = 5.830951895 Reorder the terms: -9 + v = 5.830951895 Solving -9 + v = 5.830951895 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 = 5.830951895 + 9 Combine like terms: -9 + 9 = 0 0 + v = 5.830951895 + 9 v = 5.830951895 + 9 Combine like terms: 5.830951895 + 9 = 14.830951895 v = 14.830951895 Simplifying v = 14.830951895Subproblem 2
v + -9 = -5.830951895 Simplifying v + -9 = -5.830951895 Reorder the terms: -9 + v = -5.830951895 Solving -9 + v = -5.830951895 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 = -5.830951895 + 9 Combine like terms: -9 + 9 = 0 0 + v = -5.830951895 + 9 v = -5.830951895 + 9 Combine like terms: -5.830951895 + 9 = 3.169048105 v = 3.169048105 Simplifying v = 3.169048105Solution
The solution to the problem is based on the solutions from the subproblems. v = {14.830951895, 3.169048105}
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