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Simplifying v2 + -18v = 81 Reorder the terms: -18v + v2 = 81 Solving -18v + v2 = 81 Solving for variable 'v'. Reorder the terms: -81 + -18v + v2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + -18v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -18v + 81 + v2 = 0 + 81 Reorder the terms: -81 + 81 + -18v + v2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -18v + v2 = 0 + 81 -18v + v2 = 0 + 81 Combine like terms: 0 + 81 = 81 -18v + v2 = 81 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 = 81 + 81 Reorder the terms: 81 + -18v + v2 = 81 + 81 Combine like terms: 81 + 81 = 162 81 + -18v + v2 = 162 Factor a perfect square on the left side: (v + -9)(v + -9) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (v + -9) equal to 12.727922061 and -12.727922061.Subproblem 1
v + -9 = 12.727922061 Simplifying v + -9 = 12.727922061 Reorder the terms: -9 + v = 12.727922061 Solving -9 + v = 12.727922061 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 = 12.727922061 + 9 Combine like terms: -9 + 9 = 0 0 + v = 12.727922061 + 9 v = 12.727922061 + 9 Combine like terms: 12.727922061 + 9 = 21.727922061 v = 21.727922061 Simplifying v = 21.727922061Subproblem 2
v + -9 = -12.727922061 Simplifying v + -9 = -12.727922061 Reorder the terms: -9 + v = -12.727922061 Solving -9 + v = -12.727922061 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 = -12.727922061 + 9 Combine like terms: -9 + 9 = 0 0 + v = -12.727922061 + 9 v = -12.727922061 + 9 Combine like terms: -12.727922061 + 9 = -3.727922061 v = -3.727922061 Simplifying v = -3.727922061Solution
The solution to the problem is based on the solutions from the subproblems. v = {21.727922061, -3.727922061}
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