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Simplifying 5v2 + -11v + -176 = -1v + -1 Reorder the terms: -176 + -11v + 5v2 = -1v + -1 Reorder the terms: -176 + -11v + 5v2 = -1 + -1v Solving -176 + -11v + 5v2 = -1 + -1v Solving for variable 'v'. Reorder the terms: -176 + 1 + -11v + v + 5v2 = -1 + -1v + 1 + v Combine like terms: -176 + 1 = -175 -175 + -11v + v + 5v2 = -1 + -1v + 1 + v Combine like terms: -11v + v = -10v -175 + -10v + 5v2 = -1 + -1v + 1 + v Reorder the terms: -175 + -10v + 5v2 = -1 + 1 + -1v + v Combine like terms: -1 + 1 = 0 -175 + -10v + 5v2 = 0 + -1v + v -175 + -10v + 5v2 = -1v + v Combine like terms: -1v + v = 0 -175 + -10v + 5v2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-35 + -2v + v2) = 0 Factor a trinomial. 5((-5 + -1v)(7 + -1v)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -1v)' equal to zero and attempt to solve: Simplifying -5 + -1v = 0 Solving -5 + -1v = 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 + -1v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1v = 0 + 5 -1v = 0 + 5 Combine like terms: 0 + 5 = 5 -1v = 5 Divide each side by '-1'. v = -5 Simplifying v = -5Subproblem 2
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 = 7Solution
v = {-5, 7}
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