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Simplifying v2 + 9v + -106 = 0 Reorder the terms: -106 + 9v + v2 = 0 Solving -106 + 9v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '106' to each side of the equation. -106 + 9v + 106 + v2 = 0 + 106 Reorder the terms: -106 + 106 + 9v + v2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + 9v + v2 = 0 + 106 9v + v2 = 0 + 106 Combine like terms: 0 + 106 = 106 9v + v2 = 106 The v term is 9v. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9v + 20.25 + v2 = 106 + 20.25 Reorder the terms: 20.25 + 9v + v2 = 106 + 20.25 Combine like terms: 106 + 20.25 = 126.25 20.25 + 9v + v2 = 126.25 Factor a perfect square on the left side: (v + 4.5)(v + 4.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (v + 4.5) equal to 11.236102527 and -11.236102527.Subproblem 1
v + 4.5 = 11.236102527 Simplifying v + 4.5 = 11.236102527 Reorder the terms: 4.5 + v = 11.236102527 Solving 4.5 + v = 11.236102527 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + v = 11.236102527 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = 11.236102527 + -4.5 v = 11.236102527 + -4.5 Combine like terms: 11.236102527 + -4.5 = 6.736102527 v = 6.736102527 Simplifying v = 6.736102527Subproblem 2
v + 4.5 = -11.236102527 Simplifying v + 4.5 = -11.236102527 Reorder the terms: 4.5 + v = -11.236102527 Solving 4.5 + v = -11.236102527 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + v = -11.236102527 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = -11.236102527 + -4.5 v = -11.236102527 + -4.5 Combine like terms: -11.236102527 + -4.5 = -15.736102527 v = -15.736102527 Simplifying v = -15.736102527Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.736102527, -15.736102527}
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