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Simplifying 7v2 + 40v + -14 = 2v2 + 7v Reorder the terms: -14 + 40v + 7v2 = 2v2 + 7v Reorder the terms: -14 + 40v + 7v2 = 7v + 2v2 Solving -14 + 40v + 7v2 = 7v + 2v2 Solving for variable 'v'. Reorder the terms: -14 + 40v + -7v + 7v2 + -2v2 = 7v + 2v2 + -7v + -2v2 Combine like terms: 40v + -7v = 33v -14 + 33v + 7v2 + -2v2 = 7v + 2v2 + -7v + -2v2 Combine like terms: 7v2 + -2v2 = 5v2 -14 + 33v + 5v2 = 7v + 2v2 + -7v + -2v2 Reorder the terms: -14 + 33v + 5v2 = 7v + -7v + 2v2 + -2v2 Combine like terms: 7v + -7v = 0 -14 + 33v + 5v2 = 0 + 2v2 + -2v2 -14 + 33v + 5v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 -14 + 33v + 5v2 = 0 Factor a trinomial. (-7 + -1v)(2 + -5v) = 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 + -5v)' equal to zero and attempt to solve: Simplifying 2 + -5v = 0 Solving 2 + -5v = 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 + -5v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5v = 0 + -2 -5v = 0 + -2 Combine like terms: 0 + -2 = -2 -5v = -2 Divide each side by '-5'. v = 0.4 Simplifying v = 0.4Solution
v = {-7, 0.4}
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