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Simplifying 2v2 + 15v + 11 + -1v2 + -10v + -25 = 0 Reorder the terms: 11 + -25 + 15v + -10v + 2v2 + -1v2 = 0 Combine like terms: 11 + -25 = -14 -14 + 15v + -10v + 2v2 + -1v2 = 0 Combine like terms: 15v + -10v = 5v -14 + 5v + 2v2 + -1v2 = 0 Combine like terms: 2v2 + -1v2 = 1v2 -14 + 5v + 1v2 = 0 Solving -14 + 5v + 1v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + -1v)(2 + -1v) = 0Subproblem 1
Set the factor '(-7 + -1v)' equal to zero and attempt to solve: Simplifying -7 + -1v = 0 Solving -7 + -1v = 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 + -1v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1v = 0 + 7 -1v = 0 + 7 Combine like terms: 0 + 7 = 7 -1v = 7 Divide each side by '-1'. v = -7 Simplifying v = -7Subproblem 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 = {-7, 2}
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