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Simplifying 4v2 + -9 = 6v Reorder the terms: -9 + 4v2 = 6v Solving -9 + 4v2 = 6v Solving for variable 'v'. Reorder the terms: -9 + -6v + 4v2 = 6v + -6v Combine like terms: 6v + -6v = 0 -9 + -6v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -1.5v + v2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1.5v + 2.25 + v2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1.5v + v2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1.5v + v2 = 0 + 2.25 -1.5v + v2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1.5v + v2 = 2.25 The v term is -1.5v. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5v + 0.5625 + v2 = 2.25 + 0.5625 Reorder the terms: 0.5625 + -1.5v + v2 = 2.25 + 0.5625 Combine like terms: 2.25 + 0.5625 = 2.8125 0.5625 + -1.5v + v2 = 2.8125 Factor a perfect square on the left side: (v + -0.75)(v + -0.75) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (v + -0.75) equal to 1.677050983 and -1.677050983.Subproblem 1
v + -0.75 = 1.677050983 Simplifying v + -0.75 = 1.677050983 Reorder the terms: -0.75 + v = 1.677050983 Solving -0.75 + v = 1.677050983 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + v = 1.677050983 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + v = 1.677050983 + 0.75 v = 1.677050983 + 0.75 Combine like terms: 1.677050983 + 0.75 = 2.427050983 v = 2.427050983 Simplifying v = 2.427050983Subproblem 2
v + -0.75 = -1.677050983 Simplifying v + -0.75 = -1.677050983 Reorder the terms: -0.75 + v = -1.677050983 Solving -0.75 + v = -1.677050983 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + v = -1.677050983 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + v = -1.677050983 + 0.75 v = -1.677050983 + 0.75 Combine like terms: -1.677050983 + 0.75 = -0.927050983 v = -0.927050983 Simplifying v = -0.927050983Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.427050983, -0.927050983}
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