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Simplifying 7v2 + 34v + -45 = 3 Reorder the terms: -45 + 34v + 7v2 = 3 Solving -45 + 34v + 7v2 = 3 Solving for variable 'v'. Reorder the terms: -45 + -3 + 34v + 7v2 = 3 + -3 Combine like terms: -45 + -3 = -48 -48 + 34v + 7v2 = 3 + -3 Combine like terms: 3 + -3 = 0 -48 + 34v + 7v2 = 0 Factor a trinomial. (-6 + -1v)(8 + -7v) = 0Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve: Simplifying -6 + -1v = 0 Solving -6 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1v = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1v = 0 + 6 -1v = 0 + 6 Combine like terms: 0 + 6 = 6 -1v = 6 Divide each side by '-1'. v = -6 Simplifying v = -6Subproblem 2
Set the factor '(8 + -7v)' equal to zero and attempt to solve: Simplifying 8 + -7v = 0 Solving 8 + -7v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7v = 0 + -8 -7v = 0 + -8 Combine like terms: 0 + -8 = -8 -7v = -8 Divide each side by '-7'. v = 1.142857143 Simplifying v = 1.142857143Solution
v = {-6, 1.142857143}
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