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Simplifying v2 + 14v = 28 Reorder the terms: 14v + v2 = 28 Solving 14v + v2 = 28 Solving for variable 'v'. Reorder the terms: -28 + 14v + v2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 14v + 28 + v2 = 0 + 28 Reorder the terms: -28 + 28 + 14v + v2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 14v + v2 = 0 + 28 14v + v2 = 0 + 28 Combine like terms: 0 + 28 = 28 14v + v2 = 28 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 = 28 + 49 Reorder the terms: 49 + 14v + v2 = 28 + 49 Combine like terms: 28 + 49 = 77 49 + 14v + v2 = 77 Factor a perfect square on the left side: (v + 7)(v + 7) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (v + 7) equal to 8.774964387 and -8.774964387.Subproblem 1
v + 7 = 8.774964387 Simplifying v + 7 = 8.774964387 Reorder the terms: 7 + v = 8.774964387 Solving 7 + v = 8.774964387 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 = 8.774964387 + -7 Combine like terms: 7 + -7 = 0 0 + v = 8.774964387 + -7 v = 8.774964387 + -7 Combine like terms: 8.774964387 + -7 = 1.774964387 v = 1.774964387 Simplifying v = 1.774964387Subproblem 2
v + 7 = -8.774964387 Simplifying v + 7 = -8.774964387 Reorder the terms: 7 + v = -8.774964387 Solving 7 + v = -8.774964387 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 = -8.774964387 + -7 Combine like terms: 7 + -7 = 0 0 + v = -8.774964387 + -7 v = -8.774964387 + -7 Combine like terms: -8.774964387 + -7 = -15.774964387 v = -15.774964387 Simplifying v = -15.774964387Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.774964387, -15.774964387}
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