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Simplifying v2 + 28v + 32 = 0 Reorder the terms: 32 + 28v + v2 = 0 Solving 32 + 28v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 28v + -32 + v2 = 0 + -32 Reorder the terms: 32 + -32 + 28v + v2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 28v + v2 = 0 + -32 28v + v2 = 0 + -32 Combine like terms: 0 + -32 = -32 28v + v2 = -32 The v term is 28v. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28v + 196 + v2 = -32 + 196 Reorder the terms: 196 + 28v + v2 = -32 + 196 Combine like terms: -32 + 196 = 164 196 + 28v + v2 = 164 Factor a perfect square on the left side: (v + 14)(v + 14) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (v + 14) equal to 12.806248475 and -12.806248475.Subproblem 1
v + 14 = 12.806248475 Simplifying v + 14 = 12.806248475 Reorder the terms: 14 + v = 12.806248475 Solving 14 + v = 12.806248475 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + v = 12.806248475 + -14 Combine like terms: 14 + -14 = 0 0 + v = 12.806248475 + -14 v = 12.806248475 + -14 Combine like terms: 12.806248475 + -14 = -1.193751525 v = -1.193751525 Simplifying v = -1.193751525Subproblem 2
v + 14 = -12.806248475 Simplifying v + 14 = -12.806248475 Reorder the terms: 14 + v = -12.806248475 Solving 14 + v = -12.806248475 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + v = -12.806248475 + -14 Combine like terms: 14 + -14 = 0 0 + v = -12.806248475 + -14 v = -12.806248475 + -14 Combine like terms: -12.806248475 + -14 = -26.806248475 v = -26.806248475 Simplifying v = -26.806248475Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.193751525, -26.806248475}
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