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Simplifying -7v2 + -13v = 8 + -9v + -11v2 Reorder the terms: -13v + -7v2 = 8 + -9v + -11v2 Solving -13v + -7v2 = 8 + -9v + -11v2 Solving for variable 'v'. Reorder the terms: -8 + -13v + 9v + -7v2 + 11v2 = 8 + -9v + -11v2 + -8 + 9v + 11v2 Combine like terms: -13v + 9v = -4v -8 + -4v + -7v2 + 11v2 = 8 + -9v + -11v2 + -8 + 9v + 11v2 Combine like terms: -7v2 + 11v2 = 4v2 -8 + -4v + 4v2 = 8 + -9v + -11v2 + -8 + 9v + 11v2 Reorder the terms: -8 + -4v + 4v2 = 8 + -8 + -9v + 9v + -11v2 + 11v2 Combine like terms: 8 + -8 = 0 -8 + -4v + 4v2 = 0 + -9v + 9v + -11v2 + 11v2 -8 + -4v + 4v2 = -9v + 9v + -11v2 + 11v2 Combine like terms: -9v + 9v = 0 -8 + -4v + 4v2 = 0 + -11v2 + 11v2 -8 + -4v + 4v2 = -11v2 + 11v2 Combine like terms: -11v2 + 11v2 = 0 -8 + -4v + 4v2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + -1v + v2) = 0 Factor a trinomial. 4((-1 + -1v)(2 + -1v)) = 0 Ignore the factor 4.Subproblem 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 '(2 + -1v)' equal to zero and attempt to solve: Simplifying 2 + -1v = 0 Solving 2 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1v = 0 + -2 -1v = 0 + -2 Combine like terms: 0 + -2 = -2 -1v = -2 Divide each side by '-1'. v = 2 Simplifying v = 2Solution
v = {-1, 2}
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