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Simplifying 5v2 + v + 1 = 3v + 2 Reorder the terms: 1 + v + 5v2 = 3v + 2 Reorder the terms: 1 + v + 5v2 = 2 + 3v Solving 1 + v + 5v2 = 2 + 3v Solving for variable 'v'. Reorder the terms: 1 + -2 + v + -3v + 5v2 = 2 + 3v + -2 + -3v Combine like terms: 1 + -2 = -1 -1 + v + -3v + 5v2 = 2 + 3v + -2 + -3v Combine like terms: v + -3v = -2v -1 + -2v + 5v2 = 2 + 3v + -2 + -3v Reorder the terms: -1 + -2v + 5v2 = 2 + -2 + 3v + -3v Combine like terms: 2 + -2 = 0 -1 + -2v + 5v2 = 0 + 3v + -3v -1 + -2v + 5v2 = 3v + -3v Combine like terms: 3v + -3v = 0 -1 + -2v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -0.4v + v2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.4v + 0.2 + v2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.4v + v2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.4v + v2 = 0 + 0.2 -0.4v + v2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.4v + v2 = 0.2 The v term is -0.4v. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4v + 0.04 + v2 = 0.2 + 0.04 Reorder the terms: 0.04 + -0.4v + v2 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + -0.4v + v2 = 0.24 Factor a perfect square on the left side: (v + -0.2)(v + -0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (v + -0.2) equal to 0.489897949 and -0.489897949.Subproblem 1
v + -0.2 = 0.489897949 Simplifying v + -0.2 = 0.489897949 Reorder the terms: -0.2 + v = 0.489897949 Solving -0.2 + v = 0.489897949 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + v = 0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + v = 0.489897949 + 0.2 v = 0.489897949 + 0.2 Combine like terms: 0.489897949 + 0.2 = 0.689897949 v = 0.689897949 Simplifying v = 0.689897949Subproblem 2
v + -0.2 = -0.489897949 Simplifying v + -0.2 = -0.489897949 Reorder the terms: -0.2 + v = -0.489897949 Solving -0.2 + v = -0.489897949 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + v = -0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + v = -0.489897949 + 0.2 v = -0.489897949 + 0.2 Combine like terms: -0.489897949 + 0.2 = -0.289897949 v = -0.289897949 Simplifying v = -0.289897949Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.689897949, -0.289897949}
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