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Simplifying v2 = 18v + -23 Reorder the terms: v2 = -23 + 18v Solving v2 = -23 + 18v Solving for variable 'v'. Reorder the terms: 23 + -18v + v2 = -23 + 18v + 23 + -18v Reorder the terms: 23 + -18v + v2 = -23 + 23 + 18v + -18v Combine like terms: -23 + 23 = 0 23 + -18v + v2 = 0 + 18v + -18v 23 + -18v + v2 = 18v + -18v Combine like terms: 18v + -18v = 0 23 + -18v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + -18v + -23 + v2 = 0 + -23 Reorder the terms: 23 + -23 + -18v + v2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -18v + v2 = 0 + -23 -18v + v2 = 0 + -23 Combine like terms: 0 + -23 = -23 -18v + v2 = -23 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 = -23 + 81 Reorder the terms: 81 + -18v + v2 = -23 + 81 Combine like terms: -23 + 81 = 58 81 + -18v + v2 = 58 Factor a perfect square on the left side: (v + -9)(v + -9) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (v + -9) equal to 7.615773106 and -7.615773106.Subproblem 1
v + -9 = 7.615773106 Simplifying v + -9 = 7.615773106 Reorder the terms: -9 + v = 7.615773106 Solving -9 + v = 7.615773106 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 = 7.615773106 + 9 Combine like terms: -9 + 9 = 0 0 + v = 7.615773106 + 9 v = 7.615773106 + 9 Combine like terms: 7.615773106 + 9 = 16.615773106 v = 16.615773106 Simplifying v = 16.615773106Subproblem 2
v + -9 = -7.615773106 Simplifying v + -9 = -7.615773106 Reorder the terms: -9 + v = -7.615773106 Solving -9 + v = -7.615773106 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 = -7.615773106 + 9 Combine like terms: -9 + 9 = 0 0 + v = -7.615773106 + 9 v = -7.615773106 + 9 Combine like terms: -7.615773106 + 9 = 1.384226894 v = 1.384226894 Simplifying v = 1.384226894Solution
The solution to the problem is based on the solutions from the subproblems. v = {16.615773106, 1.384226894}
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