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Simplifying v2 + 13v + 21 = 0 Reorder the terms: 21 + 13v + v2 = 0 Solving 21 + 13v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 13v + -21 + v2 = 0 + -21 Reorder the terms: 21 + -21 + 13v + v2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 13v + v2 = 0 + -21 13v + v2 = 0 + -21 Combine like terms: 0 + -21 = -21 13v + v2 = -21 The v term is 13v. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13v + 42.25 + v2 = -21 + 42.25 Reorder the terms: 42.25 + 13v + v2 = -21 + 42.25 Combine like terms: -21 + 42.25 = 21.25 42.25 + 13v + v2 = 21.25 Factor a perfect square on the left side: (v + 6.5)(v + 6.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (v + 6.5) equal to 4.609772229 and -4.609772229.Subproblem 1
v + 6.5 = 4.609772229 Simplifying v + 6.5 = 4.609772229 Reorder the terms: 6.5 + v = 4.609772229 Solving 6.5 + v = 4.609772229 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + v = 4.609772229 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + v = 4.609772229 + -6.5 v = 4.609772229 + -6.5 Combine like terms: 4.609772229 + -6.5 = -1.890227771 v = -1.890227771 Simplifying v = -1.890227771Subproblem 2
v + 6.5 = -4.609772229 Simplifying v + 6.5 = -4.609772229 Reorder the terms: 6.5 + v = -4.609772229 Solving 6.5 + v = -4.609772229 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + v = -4.609772229 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + v = -4.609772229 + -6.5 v = -4.609772229 + -6.5 Combine like terms: -4.609772229 + -6.5 = -11.109772229 v = -11.109772229 Simplifying v = -11.109772229Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.890227771, -11.109772229}
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