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Simplifying 4v2 + 12v + -5 = 0 Reorder the terms: -5 + 12v + 4v2 = 0 Solving -5 + 12v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 3v + v2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 3v + 1.25 + v2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 3v + v2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 3v + v2 = 0 + 1.25 3v + v2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 3v + v2 = 1.25 The v term is 3v. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3v + 2.25 + v2 = 1.25 + 2.25 Reorder the terms: 2.25 + 3v + v2 = 1.25 + 2.25 Combine like terms: 1.25 + 2.25 = 3.5 2.25 + 3v + v2 = 3.5 Factor a perfect square on the left side: (v + 1.5)(v + 1.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (v + 1.5) equal to 1.870828693 and -1.870828693.Subproblem 1
v + 1.5 = 1.870828693 Simplifying v + 1.5 = 1.870828693 Reorder the terms: 1.5 + v = 1.870828693 Solving 1.5 + v = 1.870828693 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = 1.870828693 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = 1.870828693 + -1.5 v = 1.870828693 + -1.5 Combine like terms: 1.870828693 + -1.5 = 0.370828693 v = 0.370828693 Simplifying v = 0.370828693Subproblem 2
v + 1.5 = -1.870828693 Simplifying v + 1.5 = -1.870828693 Reorder the terms: 1.5 + v = -1.870828693 Solving 1.5 + v = -1.870828693 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = -1.870828693 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = -1.870828693 + -1.5 v = -1.870828693 + -1.5 Combine like terms: -1.870828693 + -1.5 = -3.370828693 v = -3.370828693 Simplifying v = -3.370828693Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.370828693, -3.370828693}
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