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Simplifying 2v2 + -18v + 41 + -1v2 + 16 = 0 Reorder the terms: 41 + 16 + -18v + 2v2 + -1v2 = 0 Combine like terms: 41 + 16 = 57 57 + -18v + 2v2 + -1v2 = 0 Combine like terms: 2v2 + -1v2 = 1v2 57 + -18v + 1v2 = 0 Solving 57 + -18v + 1v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-57' to each side of the equation. 57 + -18v + -57 + v2 = 0 + -57 Reorder the terms: 57 + -57 + -18v + v2 = 0 + -57 Combine like terms: 57 + -57 = 0 0 + -18v + v2 = 0 + -57 -18v + v2 = 0 + -57 Combine like terms: 0 + -57 = -57 -18v + v2 = -57 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 = -57 + 81 Reorder the terms: 81 + -18v + v2 = -57 + 81 Combine like terms: -57 + 81 = 24 81 + -18v + v2 = 24 Factor a perfect square on the left side: (v + -9)(v + -9) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (v + -9) equal to 4.898979486 and -4.898979486.Subproblem 1
v + -9 = 4.898979486 Simplifying v + -9 = 4.898979486 Reorder the terms: -9 + v = 4.898979486 Solving -9 + v = 4.898979486 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 = 4.898979486 + 9 Combine like terms: -9 + 9 = 0 0 + v = 4.898979486 + 9 v = 4.898979486 + 9 Combine like terms: 4.898979486 + 9 = 13.898979486 v = 13.898979486 Simplifying v = 13.898979486Subproblem 2
v + -9 = -4.898979486 Simplifying v + -9 = -4.898979486 Reorder the terms: -9 + v = -4.898979486 Solving -9 + v = -4.898979486 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 = -4.898979486 + 9 Combine like terms: -9 + 9 = 0 0 + v = -4.898979486 + 9 v = -4.898979486 + 9 Combine like terms: -4.898979486 + 9 = 4.101020514 v = 4.101020514 Simplifying v = 4.101020514Solution
The solution to the problem is based on the solutions from the subproblems. v = {13.898979486, 4.101020514}
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