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Simplifying 41v2 + -14v + -13 = -8v2 + -5 Reorder the terms: -13 + -14v + 41v2 = -8v2 + -5 Reorder the terms: -13 + -14v + 41v2 = -5 + -8v2 Solving -13 + -14v + 41v2 = -5 + -8v2 Solving for variable 'v'. Reorder the terms: -13 + 5 + -14v + 41v2 + 8v2 = -5 + -8v2 + 5 + 8v2 Combine like terms: -13 + 5 = -8 -8 + -14v + 41v2 + 8v2 = -5 + -8v2 + 5 + 8v2 Combine like terms: 41v2 + 8v2 = 49v2 -8 + -14v + 49v2 = -5 + -8v2 + 5 + 8v2 Reorder the terms: -8 + -14v + 49v2 = -5 + 5 + -8v2 + 8v2 Combine like terms: -5 + 5 = 0 -8 + -14v + 49v2 = 0 + -8v2 + 8v2 -8 + -14v + 49v2 = -8v2 + 8v2 Combine like terms: -8v2 + 8v2 = 0 -8 + -14v + 49v2 = 0 Factor a trinomial. (-2 + -7v)(4 + -7v) = 0Subproblem 1
Set the factor '(-2 + -7v)' equal to zero and attempt to solve: Simplifying -2 + -7v = 0 Solving -2 + -7v = 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 + -7v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7v = 0 + 2 -7v = 0 + 2 Combine like terms: 0 + 2 = 2 -7v = 2 Divide each side by '-7'. v = -0.2857142857 Simplifying v = -0.2857142857Subproblem 2
Set the factor '(4 + -7v)' equal to zero and attempt to solve: Simplifying 4 + -7v = 0 Solving 4 + -7v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7v = 0 + -4 -7v = 0 + -4 Combine like terms: 0 + -4 = -4 -7v = -4 Divide each side by '-7'. v = 0.5714285714 Simplifying v = 0.5714285714Solution
v = {-0.2857142857, 0.5714285714}
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