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Simplifying v(14v + 5) = 9 Reorder the terms: v(5 + 14v) = 9 (5 * v + 14v * v) = 9 (5v + 14v2) = 9 Solving 5v + 14v2 = 9 Solving for variable 'v'. Reorder the terms: -9 + 5v + 14v2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 5v + 14v2 = 0 Factor a trinomial. (-1 + -1v)(9 + -14v) = 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 '(9 + -14v)' equal to zero and attempt to solve: Simplifying 9 + -14v = 0 Solving 9 + -14v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -14v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -14v = 0 + -9 -14v = 0 + -9 Combine like terms: 0 + -9 = -9 -14v = -9 Divide each side by '-14'. v = 0.6428571429 Simplifying v = 0.6428571429Solution
v = {-1, 0.6428571429}
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