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Simplifying 10v2 + -94v + 105 = -7 Reorder the terms: 105 + -94v + 10v2 = -7 Solving 105 + -94v + 10v2 = -7 Solving for variable 'v'. Reorder the terms: 105 + 7 + -94v + 10v2 = -7 + 7 Combine like terms: 105 + 7 = 112 112 + -94v + 10v2 = -7 + 7 Combine like terms: -7 + 7 = 0 112 + -94v + 10v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(56 + -47v + 5v2) = 0 Factor a trinomial. 2((7 + -5v)(8 + -1v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -5v)' equal to zero and attempt to solve: Simplifying 7 + -5v = 0 Solving 7 + -5v = 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 + -5v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5v = 0 + -7 -5v = 0 + -7 Combine like terms: 0 + -7 = -7 -5v = -7 Divide each side by '-5'. v = 1.4 Simplifying v = 1.4Subproblem 2
Set the factor '(8 + -1v)' equal to zero and attempt to solve: Simplifying 8 + -1v = 0 Solving 8 + -1v = 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 + -1v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1v = 0 + -8 -1v = 0 + -8 Combine like terms: 0 + -8 = -8 -1v = -8 Divide each side by '-1'. v = 8 Simplifying v = 8Solution
v = {1.4, 8}
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