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Simplifying v2 + -26v = 19 Reorder the terms: -26v + v2 = 19 Solving -26v + v2 = 19 Solving for variable 'v'. Reorder the terms: -19 + -26v + v2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -26v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -26v + 19 + v2 = 0 + 19 Reorder the terms: -19 + 19 + -26v + v2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -26v + v2 = 0 + 19 -26v + v2 = 0 + 19 Combine like terms: 0 + 19 = 19 -26v + v2 = 19 The v term is -26v. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26v + 169 + v2 = 19 + 169 Reorder the terms: 169 + -26v + v2 = 19 + 169 Combine like terms: 19 + 169 = 188 169 + -26v + v2 = 188 Factor a perfect square on the left side: (v + -13)(v + -13) = 188 Calculate the square root of the right side: 13.711309201 Break this problem into two subproblems by setting (v + -13) equal to 13.711309201 and -13.711309201.Subproblem 1
v + -13 = 13.711309201 Simplifying v + -13 = 13.711309201 Reorder the terms: -13 + v = 13.711309201 Solving -13 + v = 13.711309201 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + v = 13.711309201 + 13 Combine like terms: -13 + 13 = 0 0 + v = 13.711309201 + 13 v = 13.711309201 + 13 Combine like terms: 13.711309201 + 13 = 26.711309201 v = 26.711309201 Simplifying v = 26.711309201Subproblem 2
v + -13 = -13.711309201 Simplifying v + -13 = -13.711309201 Reorder the terms: -13 + v = -13.711309201 Solving -13 + v = -13.711309201 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + v = -13.711309201 + 13 Combine like terms: -13 + 13 = 0 0 + v = -13.711309201 + 13 v = -13.711309201 + 13 Combine like terms: -13.711309201 + 13 = -0.711309201 v = -0.711309201 Simplifying v = -0.711309201Solution
The solution to the problem is based on the solutions from the subproblems. v = {26.711309201, -0.711309201}
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