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Simplifying v2 + -10v + -18 = 0 Reorder the terms: -18 + -10v + v2 = 0 Solving -18 + -10v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -10v + 18 + v2 = 0 + 18 Reorder the terms: -18 + 18 + -10v + v2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -10v + v2 = 0 + 18 -10v + v2 = 0 + 18 Combine like terms: 0 + 18 = 18 -10v + v2 = 18 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 = 18 + 25 Reorder the terms: 25 + -10v + v2 = 18 + 25 Combine like terms: 18 + 25 = 43 25 + -10v + v2 = 43 Factor a perfect square on the left side: (v + -5)(v + -5) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (v + -5) equal to 6.557438524 and -6.557438524.Subproblem 1
v + -5 = 6.557438524 Simplifying v + -5 = 6.557438524 Reorder the terms: -5 + v = 6.557438524 Solving -5 + v = 6.557438524 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 = 6.557438524 + 5 Combine like terms: -5 + 5 = 0 0 + v = 6.557438524 + 5 v = 6.557438524 + 5 Combine like terms: 6.557438524 + 5 = 11.557438524 v = 11.557438524 Simplifying v = 11.557438524Subproblem 2
v + -5 = -6.557438524 Simplifying v + -5 = -6.557438524 Reorder the terms: -5 + v = -6.557438524 Solving -5 + v = -6.557438524 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 = -6.557438524 + 5 Combine like terms: -5 + 5 = 0 0 + v = -6.557438524 + 5 v = -6.557438524 + 5 Combine like terms: -6.557438524 + 5 = -1.557438524 v = -1.557438524 Simplifying v = -1.557438524Solution
The solution to the problem is based on the solutions from the subproblems. v = {11.557438524, -1.557438524}
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