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Simplifying 5v2 + 5 = -21v Reorder the terms: 5 + 5v2 = -21v Solving 5 + 5v2 = -21v Solving for variable 'v'. Reorder the terms: 5 + 21v + 5v2 = -21v + 21v Combine like terms: -21v + 21v = 0 5 + 21v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 4.2v + v2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.2v + -1 + v2 = 0 + -1 Reorder the terms: 1 + -1 + 4.2v + v2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.2v + v2 = 0 + -1 4.2v + v2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.2v + v2 = -1 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 = -1 + 4.41 Reorder the terms: 4.41 + 4.2v + v2 = -1 + 4.41 Combine like terms: -1 + 4.41 = 3.41 4.41 + 4.2v + v2 = 3.41 Factor a perfect square on the left side: (v + 2.1)(v + 2.1) = 3.41 Calculate the square root of the right side: 1.846618531 Break this problem into two subproblems by setting (v + 2.1) equal to 1.846618531 and -1.846618531.Subproblem 1
v + 2.1 = 1.846618531 Simplifying v + 2.1 = 1.846618531 Reorder the terms: 2.1 + v = 1.846618531 Solving 2.1 + v = 1.846618531 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 = 1.846618531 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + v = 1.846618531 + -2.1 v = 1.846618531 + -2.1 Combine like terms: 1.846618531 + -2.1 = -0.253381469 v = -0.253381469 Simplifying v = -0.253381469Subproblem 2
v + 2.1 = -1.846618531 Simplifying v + 2.1 = -1.846618531 Reorder the terms: 2.1 + v = -1.846618531 Solving 2.1 + v = -1.846618531 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 = -1.846618531 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + v = -1.846618531 + -2.1 v = -1.846618531 + -2.1 Combine like terms: -1.846618531 + -2.1 = -3.946618531 v = -3.946618531 Simplifying v = -3.946618531Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.253381469, -3.946618531}
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