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Simplifying -18v = 45 + -1v2 + 6v Reorder the terms: -18v = 45 + 6v + -1v2 Solving -18v = 45 + 6v + -1v2 Solving for variable 'v'. Reorder the terms: -45 + -18v + -6v + v2 = 45 + 6v + -1v2 + -45 + -6v + v2 Combine like terms: -18v + -6v = -24v -45 + -24v + v2 = 45 + 6v + -1v2 + -45 + -6v + v2 Reorder the terms: -45 + -24v + v2 = 45 + -45 + 6v + -6v + -1v2 + v2 Combine like terms: 45 + -45 = 0 -45 + -24v + v2 = 0 + 6v + -6v + -1v2 + v2 -45 + -24v + v2 = 6v + -6v + -1v2 + v2 Combine like terms: 6v + -6v = 0 -45 + -24v + v2 = 0 + -1v2 + v2 -45 + -24v + v2 = -1v2 + v2 Combine like terms: -1v2 + v2 = 0 -45 + -24v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -24v + 45 + v2 = 0 + 45 Reorder the terms: -45 + 45 + -24v + v2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -24v + v2 = 0 + 45 -24v + v2 = 0 + 45 Combine like terms: 0 + 45 = 45 -24v + v2 = 45 The v term is -24v. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24v + 144 + v2 = 45 + 144 Reorder the terms: 144 + -24v + v2 = 45 + 144 Combine like terms: 45 + 144 = 189 144 + -24v + v2 = 189 Factor a perfect square on the left side: (v + -12)(v + -12) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (v + -12) equal to 13.747727085 and -13.747727085.Subproblem 1
v + -12 = 13.747727085 Simplifying v + -12 = 13.747727085 Reorder the terms: -12 + v = 13.747727085 Solving -12 + v = 13.747727085 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + v = 13.747727085 + 12 Combine like terms: -12 + 12 = 0 0 + v = 13.747727085 + 12 v = 13.747727085 + 12 Combine like terms: 13.747727085 + 12 = 25.747727085 v = 25.747727085 Simplifying v = 25.747727085Subproblem 2
v + -12 = -13.747727085 Simplifying v + -12 = -13.747727085 Reorder the terms: -12 + v = -13.747727085 Solving -12 + v = -13.747727085 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + v = -13.747727085 + 12 Combine like terms: -12 + 12 = 0 0 + v = -13.747727085 + 12 v = -13.747727085 + 12 Combine like terms: -13.747727085 + 12 = -1.747727085 v = -1.747727085 Simplifying v = -1.747727085Solution
The solution to the problem is based on the solutions from the subproblems. v = {25.747727085, -1.747727085}
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