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Simplifying 2v + -7 = v2 + -9 Reorder the terms: -7 + 2v = v2 + -9 Reorder the terms: -7 + 2v = -9 + v2 Solving -7 + 2v = -9 + v2 Solving for variable 'v'. Reorder the terms: -7 + 9 + 2v + -1v2 = -9 + v2 + 9 + -1v2 Combine like terms: -7 + 9 = 2 2 + 2v + -1v2 = -9 + v2 + 9 + -1v2 Reorder the terms: 2 + 2v + -1v2 = -9 + 9 + v2 + -1v2 Combine like terms: -9 + 9 = 0 2 + 2v + -1v2 = 0 + v2 + -1v2 2 + 2v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 2 + 2v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -2v + v2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + -2v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2v + v2 = 0 + 2 -2v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2v + v2 = 2 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v2 = 2 + 1 Reorder the terms: 1 + -2v + v2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2v + v2 = 3 Factor a perfect square on the left side: (v + -1)(v + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (v + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
v + -1 = 1.732050808 Simplifying v + -1 = 1.732050808 Reorder the terms: -1 + v = 1.732050808 Solving -1 + v = 1.732050808 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + v = 1.732050808 + 1 v = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 v = 2.732050808 Simplifying v = 2.732050808Subproblem 2
v + -1 = -1.732050808 Simplifying v + -1 = -1.732050808 Reorder the terms: -1 + v = -1.732050808 Solving -1 + v = -1.732050808 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + v = -1.732050808 + 1 v = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 v = -0.732050808 Simplifying v = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.732050808, -0.732050808}
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