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Simplifying (5v2 + -3v + -6) + (7v2 + -4v + 1) = 0 Reorder the terms: (-6 + -3v + 5v2) + (7v2 + -4v + 1) = 0 Remove parenthesis around (-6 + -3v + 5v2) -6 + -3v + 5v2 + (7v2 + -4v + 1) = 0 Reorder the terms: -6 + -3v + 5v2 + (1 + -4v + 7v2) = 0 Remove parenthesis around (1 + -4v + 7v2) -6 + -3v + 5v2 + 1 + -4v + 7v2 = 0 Reorder the terms: -6 + 1 + -3v + -4v + 5v2 + 7v2 = 0 Combine like terms: -6 + 1 = -5 -5 + -3v + -4v + 5v2 + 7v2 = 0 Combine like terms: -3v + -4v = -7v -5 + -7v + 5v2 + 7v2 = 0 Combine like terms: 5v2 + 7v2 = 12v2 -5 + -7v + 12v2 = 0 Solving -5 + -7v + 12v2 = 0 Solving for variable 'v'. Factor a trinomial. (-5 + -12v)(1 + -1v) = 0Subproblem 1
Set the factor '(-5 + -12v)' equal to zero and attempt to solve: Simplifying -5 + -12v = 0 Solving -5 + -12v = 0 Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -12v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -12v = 0 + 5 -12v = 0 + 5 Combine like terms: 0 + 5 = 5 -12v = 5 Divide each side by '-12'. v = -0.4166666667 Simplifying v = -0.4166666667Subproblem 2
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 = 1Solution
v = {-0.4166666667, 1}
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