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Simplifying v2 + 4v + -16 = 230 Reorder the terms: -16 + 4v + v2 = 230 Solving -16 + 4v + v2 = 230 Solving for variable 'v'. Reorder the terms: -16 + -230 + 4v + v2 = 230 + -230 Combine like terms: -16 + -230 = -246 -246 + 4v + v2 = 230 + -230 Combine like terms: 230 + -230 = 0 -246 + 4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '246' to each side of the equation. -246 + 4v + 246 + v2 = 0 + 246 Reorder the terms: -246 + 246 + 4v + v2 = 0 + 246 Combine like terms: -246 + 246 = 0 0 + 4v + v2 = 0 + 246 4v + v2 = 0 + 246 Combine like terms: 0 + 246 = 246 4v + v2 = 246 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = 246 + 4 Reorder the terms: 4 + 4v + v2 = 246 + 4 Combine like terms: 246 + 4 = 250 4 + 4v + v2 = 250 Factor a perfect square on the left side: (v + 2)(v + 2) = 250 Calculate the square root of the right side: 15.811388301 Break this problem into two subproblems by setting (v + 2) equal to 15.811388301 and -15.811388301.Subproblem 1
v + 2 = 15.811388301 Simplifying v + 2 = 15.811388301 Reorder the terms: 2 + v = 15.811388301 Solving 2 + v = 15.811388301 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 15.811388301 + -2 Combine like terms: 2 + -2 = 0 0 + v = 15.811388301 + -2 v = 15.811388301 + -2 Combine like terms: 15.811388301 + -2 = 13.811388301 v = 13.811388301 Simplifying v = 13.811388301Subproblem 2
v + 2 = -15.811388301 Simplifying v + 2 = -15.811388301 Reorder the terms: 2 + v = -15.811388301 Solving 2 + v = -15.811388301 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = -15.811388301 + -2 Combine like terms: 2 + -2 = 0 0 + v = -15.811388301 + -2 v = -15.811388301 + -2 Combine like terms: -15.811388301 + -2 = -17.811388301 v = -17.811388301 Simplifying v = -17.811388301Solution
The solution to the problem is based on the solutions from the subproblems. v = {13.811388301, -17.811388301}
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