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Simplifying (3v + 2)(3v + 2) + -1(v + 5)(v + 5) = 0 Reorder the terms: (2 + 3v)(3v + 2) + -1(v + 5)(v + 5) = 0 Reorder the terms: (2 + 3v)(2 + 3v) + -1(v + 5)(v + 5) = 0 Multiply (2 + 3v) * (2 + 3v) (2(2 + 3v) + 3v * (2 + 3v)) + -1(v + 5)(v + 5) = 0 ((2 * 2 + 3v * 2) + 3v * (2 + 3v)) + -1(v + 5)(v + 5) = 0 ((4 + 6v) + 3v * (2 + 3v)) + -1(v + 5)(v + 5) = 0 (4 + 6v + (2 * 3v + 3v * 3v)) + -1(v + 5)(v + 5) = 0 (4 + 6v + (6v + 9v2)) + -1(v + 5)(v + 5) = 0 Combine like terms: 6v + 6v = 12v (4 + 12v + 9v2) + -1(v + 5)(v + 5) = 0 Reorder the terms: 4 + 12v + 9v2 + -1(5 + v)(v + 5) = 0 Reorder the terms: 4 + 12v + 9v2 + -1(5 + v)(5 + v) = 0 Multiply (5 + v) * (5 + v) 4 + 12v + 9v2 + -1(5(5 + v) + v(5 + v)) = 0 4 + 12v + 9v2 + -1((5 * 5 + v * 5) + v(5 + v)) = 0 4 + 12v + 9v2 + -1((25 + 5v) + v(5 + v)) = 0 4 + 12v + 9v2 + -1(25 + 5v + (5 * v + v * v)) = 0 4 + 12v + 9v2 + -1(25 + 5v + (5v + v2)) = 0 Combine like terms: 5v + 5v = 10v 4 + 12v + 9v2 + -1(25 + 10v + v2) = 0 4 + 12v + 9v2 + (25 * -1 + 10v * -1 + v2 * -1) = 0 4 + 12v + 9v2 + (-25 + -10v + -1v2) = 0 Reorder the terms: 4 + -25 + 12v + -10v + 9v2 + -1v2 = 0 Combine like terms: 4 + -25 = -21 -21 + 12v + -10v + 9v2 + -1v2 = 0 Combine like terms: 12v + -10v = 2v -21 + 2v + 9v2 + -1v2 = 0 Combine like terms: 9v2 + -1v2 = 8v2 -21 + 2v + 8v2 = 0 Solving -21 + 2v + 8v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + -4v)(3 + -2v) = 0Subproblem 1
Set the factor '(-7 + -4v)' equal to zero and attempt to solve: Simplifying -7 + -4v = 0 Solving -7 + -4v = 0 Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4v = 0 + 7 -4v = 0 + 7 Combine like terms: 0 + 7 = 7 -4v = 7 Divide each side by '-4'. v = -1.75 Simplifying v = -1.75Subproblem 2
Set the factor '(3 + -2v)' equal to zero and attempt to solve: Simplifying 3 + -2v = 0 Solving 3 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2v = 0 + -3 -2v = 0 + -3 Combine like terms: 0 + -3 = -3 -2v = -3 Divide each side by '-2'. v = 1.5 Simplifying v = 1.5Solution
v = {-1.75, 1.5}
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