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Simplifying (v + -1)(5v + 2) = 9(v + 3) Reorder the terms: (-1 + v)(5v + 2) = 9(v + 3) Reorder the terms: (-1 + v)(2 + 5v) = 9(v + 3) Multiply (-1 + v) * (2 + 5v) (-1(2 + 5v) + v(2 + 5v)) = 9(v + 3) ((2 * -1 + 5v * -1) + v(2 + 5v)) = 9(v + 3) ((-2 + -5v) + v(2 + 5v)) = 9(v + 3) (-2 + -5v + (2 * v + 5v * v)) = 9(v + 3) (-2 + -5v + (2v + 5v2)) = 9(v + 3) Combine like terms: -5v + 2v = -3v (-2 + -3v + 5v2) = 9(v + 3) Reorder the terms: -2 + -3v + 5v2 = 9(3 + v) -2 + -3v + 5v2 = (3 * 9 + v * 9) -2 + -3v + 5v2 = (27 + 9v) Solving -2 + -3v + 5v2 = 27 + 9v Solving for variable 'v'. Reorder the terms: -2 + -27 + -3v + -9v + 5v2 = 27 + 9v + -27 + -9v Combine like terms: -2 + -27 = -29 -29 + -3v + -9v + 5v2 = 27 + 9v + -27 + -9v Combine like terms: -3v + -9v = -12v -29 + -12v + 5v2 = 27 + 9v + -27 + -9v Reorder the terms: -29 + -12v + 5v2 = 27 + -27 + 9v + -9v Combine like terms: 27 + -27 = 0 -29 + -12v + 5v2 = 0 + 9v + -9v -29 + -12v + 5v2 = 9v + -9v Combine like terms: 9v + -9v = 0 -29 + -12v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.8 + -2.4v + v2 = 0 Move the constant term to the right: Add '5.8' to each side of the equation. -5.8 + -2.4v + 5.8 + v2 = 0 + 5.8 Reorder the terms: -5.8 + 5.8 + -2.4v + v2 = 0 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + -2.4v + v2 = 0 + 5.8 -2.4v + v2 = 0 + 5.8 Combine like terms: 0 + 5.8 = 5.8 -2.4v + v2 = 5.8 The v term is -2.4v. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4v + 1.44 + v2 = 5.8 + 1.44 Reorder the terms: 1.44 + -2.4v + v2 = 5.8 + 1.44 Combine like terms: 5.8 + 1.44 = 7.24 1.44 + -2.4v + v2 = 7.24 Factor a perfect square on the left side: (v + -1.2)(v + -1.2) = 7.24 Calculate the square root of the right side: 2.690724809 Break this problem into two subproblems by setting (v + -1.2) equal to 2.690724809 and -2.690724809.Subproblem 1
v + -1.2 = 2.690724809 Simplifying v + -1.2 = 2.690724809 Reorder the terms: -1.2 + v = 2.690724809 Solving -1.2 + v = 2.690724809 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + v = 2.690724809 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + v = 2.690724809 + 1.2 v = 2.690724809 + 1.2 Combine like terms: 2.690724809 + 1.2 = 3.890724809 v = 3.890724809 Simplifying v = 3.890724809Subproblem 2
v + -1.2 = -2.690724809 Simplifying v + -1.2 = -2.690724809 Reorder the terms: -1.2 + v = -2.690724809 Solving -1.2 + v = -2.690724809 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + v = -2.690724809 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + v = -2.690724809 + 1.2 v = -2.690724809 + 1.2 Combine like terms: -2.690724809 + 1.2 = -1.490724809 v = -1.490724809 Simplifying v = -1.490724809Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.890724809, -1.490724809}
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