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Simplifying v2 + 14v = 19 Reorder the terms: 14v + v2 = 19 Solving 14v + v2 = 19 Solving for variable 'v'. Reorder the terms: -19 + 14v + v2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 14v + 19 + v2 = 0 + 19 Reorder the terms: -19 + 19 + 14v + v2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 14v + v2 = 0 + 19 14v + v2 = 0 + 19 Combine like terms: 0 + 19 = 19 14v + v2 = 19 The v term is 14v. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14v + 49 + v2 = 19 + 49 Reorder the terms: 49 + 14v + v2 = 19 + 49 Combine like terms: 19 + 49 = 68 49 + 14v + v2 = 68 Factor a perfect square on the left side: (v + 7)(v + 7) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (v + 7) equal to 8.246211251 and -8.246211251.Subproblem 1
v + 7 = 8.246211251 Simplifying v + 7 = 8.246211251 Reorder the terms: 7 + v = 8.246211251 Solving 7 + v = 8.246211251 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 8.246211251 + -7 Combine like terms: 7 + -7 = 0 0 + v = 8.246211251 + -7 v = 8.246211251 + -7 Combine like terms: 8.246211251 + -7 = 1.246211251 v = 1.246211251 Simplifying v = 1.246211251Subproblem 2
v + 7 = -8.246211251 Simplifying v + 7 = -8.246211251 Reorder the terms: 7 + v = -8.246211251 Solving 7 + v = -8.246211251 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = -8.246211251 + -7 Combine like terms: 7 + -7 = 0 0 + v = -8.246211251 + -7 v = -8.246211251 + -7 Combine like terms: -8.246211251 + -7 = -15.246211251 v = -15.246211251 Simplifying v = -15.246211251Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.246211251, -15.246211251}
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