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Simplifying 5v2 + 10v + -16 = 0 Reorder the terms: -16 + 10v + 5v2 = 0 Solving -16 + 10v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + 2v + v2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 2v + 3.2 + v2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 2v + v2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 2v + v2 = 0 + 3.2 2v + v2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 2v + v2 = 3.2 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = 3.2 + 1 Reorder the terms: 1 + 2v + v2 = 3.2 + 1 Combine like terms: 3.2 + 1 = 4.2 1 + 2v + v2 = 4.2 Factor a perfect square on the left side: (v + 1)(v + 1) = 4.2 Calculate the square root of the right side: 2.049390153 Break this problem into two subproblems by setting (v + 1) equal to 2.049390153 and -2.049390153.Subproblem 1
v + 1 = 2.049390153 Simplifying v + 1 = 2.049390153 Reorder the terms: 1 + v = 2.049390153 Solving 1 + v = 2.049390153 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 2.049390153 + -1 Combine like terms: 1 + -1 = 0 0 + v = 2.049390153 + -1 v = 2.049390153 + -1 Combine like terms: 2.049390153 + -1 = 1.049390153 v = 1.049390153 Simplifying v = 1.049390153Subproblem 2
v + 1 = -2.049390153 Simplifying v + 1 = -2.049390153 Reorder the terms: 1 + v = -2.049390153 Solving 1 + v = -2.049390153 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -2.049390153 + -1 Combine like terms: 1 + -1 = 0 0 + v = -2.049390153 + -1 v = -2.049390153 + -1 Combine like terms: -2.049390153 + -1 = -3.049390153 v = -3.049390153 Simplifying v = -3.049390153Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.049390153, -3.049390153}
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