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Simplifying 5v2 + 10v + -18 = -5 Reorder the terms: -18 + 10v + 5v2 = -5 Solving -18 + 10v + 5v2 = -5 Solving for variable 'v'. Reorder the terms: -18 + 5 + 10v + 5v2 = -5 + 5 Combine like terms: -18 + 5 = -13 -13 + 10v + 5v2 = -5 + 5 Combine like terms: -5 + 5 = 0 -13 + 10v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 2v + v2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 2v + 2.6 + v2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 2v + v2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 2v + v2 = 0 + 2.6 2v + v2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 2v + v2 = 2.6 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 = 2.6 + 1 Reorder the terms: 1 + 2v + v2 = 2.6 + 1 Combine like terms: 2.6 + 1 = 3.6 1 + 2v + v2 = 3.6 Factor a perfect square on the left side: (v + 1)(v + 1) = 3.6 Calculate the square root of the right side: 1.897366596 Break this problem into two subproblems by setting (v + 1) equal to 1.897366596 and -1.897366596.Subproblem 1
v + 1 = 1.897366596 Simplifying v + 1 = 1.897366596 Reorder the terms: 1 + v = 1.897366596 Solving 1 + v = 1.897366596 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 = 1.897366596 + -1 Combine like terms: 1 + -1 = 0 0 + v = 1.897366596 + -1 v = 1.897366596 + -1 Combine like terms: 1.897366596 + -1 = 0.897366596 v = 0.897366596 Simplifying v = 0.897366596Subproblem 2
v + 1 = -1.897366596 Simplifying v + 1 = -1.897366596 Reorder the terms: 1 + v = -1.897366596 Solving 1 + v = -1.897366596 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 = -1.897366596 + -1 Combine like terms: 1 + -1 = 0 0 + v = -1.897366596 + -1 v = -1.897366596 + -1 Combine like terms: -1.897366596 + -1 = -2.897366596 v = -2.897366596 Simplifying v = -2.897366596Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.897366596, -2.897366596}
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