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Simplifying v2 + -19 = 10v Reorder the terms: -19 + v2 = 10v Solving -19 + v2 = 10v Solving for variable 'v'. Reorder the terms: -19 + -10v + v2 = 10v + -10v Combine like terms: 10v + -10v = 0 -19 + -10v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -10v + 19 + v2 = 0 + 19 Reorder the terms: -19 + 19 + -10v + v2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -10v + v2 = 0 + 19 -10v + v2 = 0 + 19 Combine like terms: 0 + 19 = 19 -10v + v2 = 19 The v term is -10v. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10v + 25 + v2 = 19 + 25 Reorder the terms: 25 + -10v + v2 = 19 + 25 Combine like terms: 19 + 25 = 44 25 + -10v + v2 = 44 Factor a perfect square on the left side: (v + -5)(v + -5) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (v + -5) equal to 6.633249581 and -6.633249581.Subproblem 1
v + -5 = 6.633249581 Simplifying v + -5 = 6.633249581 Reorder the terms: -5 + v = 6.633249581 Solving -5 + v = 6.633249581 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = 6.633249581 + 5 Combine like terms: -5 + 5 = 0 0 + v = 6.633249581 + 5 v = 6.633249581 + 5 Combine like terms: 6.633249581 + 5 = 11.633249581 v = 11.633249581 Simplifying v = 11.633249581Subproblem 2
v + -5 = -6.633249581 Simplifying v + -5 = -6.633249581 Reorder the terms: -5 + v = -6.633249581 Solving -5 + v = -6.633249581 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = -6.633249581 + 5 Combine like terms: -5 + 5 = 0 0 + v = -6.633249581 + 5 v = -6.633249581 + 5 Combine like terms: -6.633249581 + 5 = -1.633249581 v = -1.633249581 Simplifying v = -1.633249581Solution
The solution to the problem is based on the solutions from the subproblems. v = {11.633249581, -1.633249581}
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