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Simplifying 2v2 + -11v + -5 = (v + 5)(v + 5) Reorder the terms: -5 + -11v + 2v2 = (v + 5)(v + 5) Reorder the terms: -5 + -11v + 2v2 = (5 + v)(v + 5) Reorder the terms: -5 + -11v + 2v2 = (5 + v)(5 + v) Multiply (5 + v) * (5 + v) -5 + -11v + 2v2 = (5(5 + v) + v(5 + v)) -5 + -11v + 2v2 = ((5 * 5 + v * 5) + v(5 + v)) -5 + -11v + 2v2 = ((25 + 5v) + v(5 + v)) -5 + -11v + 2v2 = (25 + 5v + (5 * v + v * v)) -5 + -11v + 2v2 = (25 + 5v + (5v + v2)) Combine like terms: 5v + 5v = 10v -5 + -11v + 2v2 = (25 + 10v + v2) Solving -5 + -11v + 2v2 = 25 + 10v + v2 Solving for variable 'v'. Reorder the terms: -5 + -25 + -11v + -10v + 2v2 + -1v2 = 25 + 10v + v2 + -25 + -10v + -1v2 Combine like terms: -5 + -25 = -30 -30 + -11v + -10v + 2v2 + -1v2 = 25 + 10v + v2 + -25 + -10v + -1v2 Combine like terms: -11v + -10v = -21v -30 + -21v + 2v2 + -1v2 = 25 + 10v + v2 + -25 + -10v + -1v2 Combine like terms: 2v2 + -1v2 = 1v2 -30 + -21v + 1v2 = 25 + 10v + v2 + -25 + -10v + -1v2 Reorder the terms: -30 + -21v + 1v2 = 25 + -25 + 10v + -10v + v2 + -1v2 Combine like terms: 25 + -25 = 0 -30 + -21v + 1v2 = 0 + 10v + -10v + v2 + -1v2 -30 + -21v + 1v2 = 10v + -10v + v2 + -1v2 Combine like terms: 10v + -10v = 0 -30 + -21v + 1v2 = 0 + v2 + -1v2 -30 + -21v + 1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -30 + -21v + 1v2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -21v + 30 + v2 = 0 + 30 Reorder the terms: -30 + 30 + -21v + v2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -21v + v2 = 0 + 30 -21v + v2 = 0 + 30 Combine like terms: 0 + 30 = 30 -21v + v2 = 30 The v term is -21v. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21v + 110.25 + v2 = 30 + 110.25 Reorder the terms: 110.25 + -21v + v2 = 30 + 110.25 Combine like terms: 30 + 110.25 = 140.25 110.25 + -21v + v2 = 140.25 Factor a perfect square on the left side: (v + -10.5)(v + -10.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (v + -10.5) equal to 11.842719282 and -11.842719282.Subproblem 1
v + -10.5 = 11.842719282 Simplifying v + -10.5 = 11.842719282 Reorder the terms: -10.5 + v = 11.842719282 Solving -10.5 + v = 11.842719282 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + v = 11.842719282 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + v = 11.842719282 + 10.5 v = 11.842719282 + 10.5 Combine like terms: 11.842719282 + 10.5 = 22.342719282 v = 22.342719282 Simplifying v = 22.342719282Subproblem 2
v + -10.5 = -11.842719282 Simplifying v + -10.5 = -11.842719282 Reorder the terms: -10.5 + v = -11.842719282 Solving -10.5 + v = -11.842719282 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + v = -11.842719282 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + v = -11.842719282 + 10.5 v = -11.842719282 + 10.5 Combine like terms: -11.842719282 + 10.5 = -1.342719282 v = -1.342719282 Simplifying v = -1.342719282Solution
The solution to the problem is based on the solutions from the subproblems. v = {22.342719282, -1.342719282}
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