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Simplifying 6v2 + -11v + -2 = v2 + -16v + 20 Reorder the terms: -2 + -11v + 6v2 = v2 + -16v + 20 Reorder the terms: -2 + -11v + 6v2 = 20 + -16v + v2 Solving -2 + -11v + 6v2 = 20 + -16v + v2 Solving for variable 'v'. Reorder the terms: -2 + -20 + -11v + 16v + 6v2 + -1v2 = 20 + -16v + v2 + -20 + 16v + -1v2 Combine like terms: -2 + -20 = -22 -22 + -11v + 16v + 6v2 + -1v2 = 20 + -16v + v2 + -20 + 16v + -1v2 Combine like terms: -11v + 16v = 5v -22 + 5v + 6v2 + -1v2 = 20 + -16v + v2 + -20 + 16v + -1v2 Combine like terms: 6v2 + -1v2 = 5v2 -22 + 5v + 5v2 = 20 + -16v + v2 + -20 + 16v + -1v2 Reorder the terms: -22 + 5v + 5v2 = 20 + -20 + -16v + 16v + v2 + -1v2 Combine like terms: 20 + -20 = 0 -22 + 5v + 5v2 = 0 + -16v + 16v + v2 + -1v2 -22 + 5v + 5v2 = -16v + 16v + v2 + -1v2 Combine like terms: -16v + 16v = 0 -22 + 5v + 5v2 = 0 + v2 + -1v2 -22 + 5v + 5v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -22 + 5v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.4 + v + v2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + v + 4.4 + v2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + v + v2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + v + v2 = 0 + 4.4 v + v2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 v + v2 = 4.4 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + v2 = 4.4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = 4.4 + 0.25 Combine like terms: 4.4 + 0.25 = 4.65 1.25 + v2 = 4.65 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 4.65 Calculate the square root of the right side: 2.156385865 Break this problem into two subproblems by setting (v + 0.5) equal to 2.156385865 and -2.156385865.Subproblem 1
v + 0.5 = 2.156385865 Simplifying v + 0.5 = 2.156385865 Reorder the terms: 0.5 + v = 2.156385865 Solving 0.5 + v = 2.156385865 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = 2.156385865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 2.156385865 + -0.5 v = 2.156385865 + -0.5 Combine like terms: 2.156385865 + -0.5 = 1.656385865 v = 1.656385865 Simplifying v = 1.656385865Subproblem 2
v + 0.5 = -2.156385865 Simplifying v + 0.5 = -2.156385865 Reorder the terms: 0.5 + v = -2.156385865 Solving 0.5 + v = -2.156385865 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = -2.156385865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -2.156385865 + -0.5 v = -2.156385865 + -0.5 Combine like terms: -2.156385865 + -0.5 = -2.656385865 v = -2.656385865 Simplifying v = -2.656385865Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.656385865, -2.656385865}
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