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Simplifying 2v2 + v + 22 + -1(v + 4)(v + 4) = 0 Reorder the terms: 2v2 + v + 22 + -1(4 + v)(v + 4) = 0 Reorder the terms: 2v2 + v + 22 + -1(4 + v)(4 + v) = 0 Multiply (4 + v) * (4 + v) 2v2 + v + 22 + -1(4(4 + v) + v(4 + v)) = 0 2v2 + v + 22 + -1((4 * 4 + v * 4) + v(4 + v)) = 0 2v2 + v + 22 + -1((16 + 4v) + v(4 + v)) = 0 2v2 + v + 22 + -1(16 + 4v + (4 * v + v * v)) = 0 2v2 + v + 22 + -1(16 + 4v + (4v + v2)) = 0 Combine like terms: 4v + 4v = 8v 2v2 + v + 22 + -1(16 + 8v + v2) = 0 2v2 + v + 22 + (16 * -1 + 8v * -1 + v2 * -1) = 0 2v2 + v + 22 + (-16 + -8v + -1v2) = 0 Reorder the terms: 22 + -16 + v + -8v + 2v2 + -1v2 = 0 Combine like terms: 22 + -16 = 6 6 + v + -8v + 2v2 + -1v2 = 0 Combine like terms: v + -8v = -7v 6 + -7v + 2v2 + -1v2 = 0 Combine like terms: 2v2 + -1v2 = 1v2 6 + -7v + 1v2 = 0 Solving 6 + -7v + 1v2 = 0 Solving for variable 'v'. Factor a trinomial. (1 + -1v)(6 + -1v) = 0Subproblem 1
Set the factor '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve: Simplifying 6 + -1v = 0 Solving 6 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1v = 0 + -6 -1v = 0 + -6 Combine like terms: 0 + -6 = -6 -1v = -6 Divide each side by '-1'. v = 6 Simplifying v = 6Solution
v = {1, 6}
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