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Simplifying v2 + 12v + 42 = 7 Reorder the terms: 42 + 12v + v2 = 7 Solving 42 + 12v + v2 = 7 Solving for variable 'v'. Reorder the terms: 42 + -7 + 12v + v2 = 7 + -7 Combine like terms: 42 + -7 = 35 35 + 12v + v2 = 7 + -7 Combine like terms: 7 + -7 = 0 35 + 12v + v2 = 0 Factor a trinomial. (7 + v)(5 + v) = 0Subproblem 1
Set the factor '(7 + v)' equal to zero and attempt to solve: Simplifying 7 + v = 0 Solving 7 + v = 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 + v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + v = 0 + -7 v = 0 + -7 Combine like terms: 0 + -7 = -7 v = -7 Simplifying v = -7Subproblem 2
Set the factor '(5 + v)' equal to zero and attempt to solve: Simplifying 5 + v = 0 Solving 5 + v = 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 + v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + v = 0 + -5 v = 0 + -5 Combine like terms: 0 + -5 = -5 v = -5 Simplifying v = -5Solution
v = {-7, -5}
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