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Simplifying v2 = 18v + -24 Reorder the terms: v2 = -24 + 18v Solving v2 = -24 + 18v Solving for variable 'v'. Reorder the terms: 24 + -18v + v2 = -24 + 18v + 24 + -18v Reorder the terms: 24 + -18v + v2 = -24 + 24 + 18v + -18v Combine like terms: -24 + 24 = 0 24 + -18v + v2 = 0 + 18v + -18v 24 + -18v + v2 = 18v + -18v Combine like terms: 18v + -18v = 0 24 + -18v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -18v + -24 + v2 = 0 + -24 Reorder the terms: 24 + -24 + -18v + v2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -18v + v2 = 0 + -24 -18v + v2 = 0 + -24 Combine like terms: 0 + -24 = -24 -18v + v2 = -24 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 = -24 + 81 Reorder the terms: 81 + -18v + v2 = -24 + 81 Combine like terms: -24 + 81 = 57 81 + -18v + v2 = 57 Factor a perfect square on the left side: (v + -9)(v + -9) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (v + -9) equal to 7.549834435 and -7.549834435.Subproblem 1
v + -9 = 7.549834435 Simplifying v + -9 = 7.549834435 Reorder the terms: -9 + v = 7.549834435 Solving -9 + v = 7.549834435 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 = 7.549834435 + 9 Combine like terms: -9 + 9 = 0 0 + v = 7.549834435 + 9 v = 7.549834435 + 9 Combine like terms: 7.549834435 + 9 = 16.549834435 v = 16.549834435 Simplifying v = 16.549834435Subproblem 2
v + -9 = -7.549834435 Simplifying v + -9 = -7.549834435 Reorder the terms: -9 + v = -7.549834435 Solving -9 + v = -7.549834435 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 = -7.549834435 + 9 Combine like terms: -9 + 9 = 0 0 + v = -7.549834435 + 9 v = -7.549834435 + 9 Combine like terms: -7.549834435 + 9 = 1.450165565 v = 1.450165565 Simplifying v = 1.450165565Solution
The solution to the problem is based on the solutions from the subproblems. v = {16.549834435, 1.450165565}
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