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Simplifying 4v2 + 12v + -9 = 0 Reorder the terms: -9 + 12v + 4v2 = 0 Solving -9 + 12v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 3v + v2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 3v + 2.25 + v2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 3v + v2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 3v + v2 = 0 + 2.25 3v + v2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 3v + v2 = 2.25 The v term is 3v. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3v + 2.25 + v2 = 2.25 + 2.25 Reorder the terms: 2.25 + 3v + v2 = 2.25 + 2.25 Combine like terms: 2.25 + 2.25 = 4.5 2.25 + 3v + v2 = 4.5 Factor a perfect square on the left side: (v + 1.5)(v + 1.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (v + 1.5) equal to 2.121320344 and -2.121320344.Subproblem 1
v + 1.5 = 2.121320344 Simplifying v + 1.5 = 2.121320344 Reorder the terms: 1.5 + v = 2.121320344 Solving 1.5 + v = 2.121320344 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = 2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = 2.121320344 + -1.5 v = 2.121320344 + -1.5 Combine like terms: 2.121320344 + -1.5 = 0.621320344 v = 0.621320344 Simplifying v = 0.621320344Subproblem 2
v + 1.5 = -2.121320344 Simplifying v + 1.5 = -2.121320344 Reorder the terms: 1.5 + v = -2.121320344 Solving 1.5 + v = -2.121320344 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = -2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = -2.121320344 + -1.5 v = -2.121320344 + -1.5 Combine like terms: -2.121320344 + -1.5 = -3.621320344 v = -3.621320344 Simplifying v = -3.621320344Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.621320344, -3.621320344}
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