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Simplifying 14v2 + -17v = 15 Reorder the terms: -17v + 14v2 = 15 Solving -17v + 14v2 = 15 Solving for variable 'v'. Reorder the terms: -15 + -17v + 14v2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -17v + 14v2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.071428571 + -1.214285714v + v2 = 0 Move the constant term to the right: Add '1.071428571' to each side of the equation. -1.071428571 + -1.214285714v + 1.071428571 + v2 = 0 + 1.071428571 Reorder the terms: -1.071428571 + 1.071428571 + -1.214285714v + v2 = 0 + 1.071428571 Combine like terms: -1.071428571 + 1.071428571 = 0.000000000 0.000000000 + -1.214285714v + v2 = 0 + 1.071428571 -1.214285714v + v2 = 0 + 1.071428571 Combine like terms: 0 + 1.071428571 = 1.071428571 -1.214285714v + v2 = 1.071428571 The v term is -1.214285714v. Take half its coefficient (-0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. -1.214285714v + 0.3686224488 + v2 = 1.071428571 + 0.3686224488 Reorder the terms: 0.3686224488 + -1.214285714v + v2 = 1.071428571 + 0.3686224488 Combine like terms: 1.071428571 + 0.3686224488 = 1.4400510198 0.3686224488 + -1.214285714v + v2 = 1.4400510198 Factor a perfect square on the left side: (v + -0.607142857)(v + -0.607142857) = 1.4400510198 Calculate the square root of the right side: 1.200021258 Break this problem into two subproblems by setting (v + -0.607142857) equal to 1.200021258 and -1.200021258.Subproblem 1
v + -0.607142857 = 1.200021258 Simplifying v + -0.607142857 = 1.200021258 Reorder the terms: -0.607142857 + v = 1.200021258 Solving -0.607142857 + v = 1.200021258 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.607142857' to each side of the equation. -0.607142857 + 0.607142857 + v = 1.200021258 + 0.607142857 Combine like terms: -0.607142857 + 0.607142857 = 0.000000000 0.000000000 + v = 1.200021258 + 0.607142857 v = 1.200021258 + 0.607142857 Combine like terms: 1.200021258 + 0.607142857 = 1.807164115 v = 1.807164115 Simplifying v = 1.807164115Subproblem 2
v + -0.607142857 = -1.200021258 Simplifying v + -0.607142857 = -1.200021258 Reorder the terms: -0.607142857 + v = -1.200021258 Solving -0.607142857 + v = -1.200021258 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.607142857' to each side of the equation. -0.607142857 + 0.607142857 + v = -1.200021258 + 0.607142857 Combine like terms: -0.607142857 + 0.607142857 = 0.000000000 0.000000000 + v = -1.200021258 + 0.607142857 v = -1.200021258 + 0.607142857 Combine like terms: -1.200021258 + 0.607142857 = -0.592878401 v = -0.592878401 Simplifying v = -0.592878401Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.807164115, -0.592878401}
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