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Simplifying 5v2 + 21v = 4 Reorder the terms: 21v + 5v2 = 4 Solving 21v + 5v2 = 4 Solving for variable 'v'. Reorder the terms: -4 + 21v + 5v2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 21v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 4.2v + v2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 4.2v + 0.8 + v2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 4.2v + v2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 4.2v + v2 = 0 + 0.8 4.2v + v2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 4.2v + v2 = 0.8 The v term is 4.2v. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2v + 4.41 + v2 = 0.8 + 4.41 Reorder the terms: 4.41 + 4.2v + v2 = 0.8 + 4.41 Combine like terms: 0.8 + 4.41 = 5.21 4.41 + 4.2v + v2 = 5.21 Factor a perfect square on the left side: (v + 2.1)(v + 2.1) = 5.21 Calculate the square root of the right side: 2.282542442 Break this problem into two subproblems by setting (v + 2.1) equal to 2.282542442 and -2.282542442.Subproblem 1
v + 2.1 = 2.282542442 Simplifying v + 2.1 = 2.282542442 Reorder the terms: 2.1 + v = 2.282542442 Solving 2.1 + v = 2.282542442 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + v = 2.282542442 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + v = 2.282542442 + -2.1 v = 2.282542442 + -2.1 Combine like terms: 2.282542442 + -2.1 = 0.182542442 v = 0.182542442 Simplifying v = 0.182542442Subproblem 2
v + 2.1 = -2.282542442 Simplifying v + 2.1 = -2.282542442 Reorder the terms: 2.1 + v = -2.282542442 Solving 2.1 + v = -2.282542442 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + v = -2.282542442 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + v = -2.282542442 + -2.1 v = -2.282542442 + -2.1 Combine like terms: -2.282542442 + -2.1 = -4.382542442 v = -4.382542442 Simplifying v = -4.382542442Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.182542442, -4.382542442}
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