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Simplifying 9v2 + -30v + 5 = 0 Reorder the terms: 5 + -30v + 9v2 = 0 Solving 5 + -30v + 9v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + -3.333333333v + v2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -3.333333333v + -0.5555555556 + v2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -3.333333333v + v2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -3.333333333v + v2 = 0 + -0.5555555556 -3.333333333v + v2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -3.333333333v + v2 = -0.5555555556 The v term is -3.333333333v. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333v + 2.777777779 + v2 = -0.5555555556 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333v + v2 = -0.5555555556 + 2.777777779 Combine like terms: -0.5555555556 + 2.777777779 = 2.2222222234 2.777777779 + -3.333333333v + v2 = 2.2222222234 Factor a perfect square on the left side: (v + -1.666666667)(v + -1.666666667) = 2.2222222234 Calculate the square root of the right side: 1.490711985 Break this problem into two subproblems by setting (v + -1.666666667) equal to 1.490711985 and -1.490711985.Subproblem 1
v + -1.666666667 = 1.490711985 Simplifying v + -1.666666667 = 1.490711985 Reorder the terms: -1.666666667 + v = 1.490711985 Solving -1.666666667 + v = 1.490711985 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + v = 1.490711985 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + v = 1.490711985 + 1.666666667 v = 1.490711985 + 1.666666667 Combine like terms: 1.490711985 + 1.666666667 = 3.157378652 v = 3.157378652 Simplifying v = 3.157378652Subproblem 2
v + -1.666666667 = -1.490711985 Simplifying v + -1.666666667 = -1.490711985 Reorder the terms: -1.666666667 + v = -1.490711985 Solving -1.666666667 + v = -1.490711985 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + v = -1.490711985 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + v = -1.490711985 + 1.666666667 v = -1.490711985 + 1.666666667 Combine like terms: -1.490711985 + 1.666666667 = 0.175954682 v = 0.175954682 Simplifying v = 0.175954682Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.157378652, 0.175954682}
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