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Simplifying v2 + -41 = 4 + 18v Reorder the terms: -41 + v2 = 4 + 18v Solving -41 + v2 = 4 + 18v Solving for variable 'v'. Reorder the terms: -41 + -4 + -18v + v2 = 4 + 18v + -4 + -18v Combine like terms: -41 + -4 = -45 -45 + -18v + v2 = 4 + 18v + -4 + -18v Reorder the terms: -45 + -18v + v2 = 4 + -4 + 18v + -18v Combine like terms: 4 + -4 = 0 -45 + -18v + v2 = 0 + 18v + -18v -45 + -18v + v2 = 18v + -18v Combine like terms: 18v + -18v = 0 -45 + -18v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -18v + 45 + v2 = 0 + 45 Reorder the terms: -45 + 45 + -18v + v2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -18v + v2 = 0 + 45 -18v + v2 = 0 + 45 Combine like terms: 0 + 45 = 45 -18v + v2 = 45 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 = 45 + 81 Reorder the terms: 81 + -18v + v2 = 45 + 81 Combine like terms: 45 + 81 = 126 81 + -18v + v2 = 126 Factor a perfect square on the left side: (v + -9)(v + -9) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (v + -9) equal to 11.22497216 and -11.22497216.Subproblem 1
v + -9 = 11.22497216 Simplifying v + -9 = 11.22497216 Reorder the terms: -9 + v = 11.22497216 Solving -9 + v = 11.22497216 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 = 11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + v = 11.22497216 + 9 v = 11.22497216 + 9 Combine like terms: 11.22497216 + 9 = 20.22497216 v = 20.22497216 Simplifying v = 20.22497216Subproblem 2
v + -9 = -11.22497216 Simplifying v + -9 = -11.22497216 Reorder the terms: -9 + v = -11.22497216 Solving -9 + v = -11.22497216 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 = -11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + v = -11.22497216 + 9 v = -11.22497216 + 9 Combine like terms: -11.22497216 + 9 = -2.22497216 v = -2.22497216 Simplifying v = -2.22497216Solution
The solution to the problem is based on the solutions from the subproblems. v = {20.22497216, -2.22497216}
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