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Simplifying 10V2 + -15V = 27 + 4V2 + -6V Reorder the terms: -15V + 10V2 = 27 + 4V2 + -6V Reorder the terms: -15V + 10V2 = 27 + -6V + 4V2 Solving -15V + 10V2 = 27 + -6V + 4V2 Solving for variable 'V'. Reorder the terms: -27 + -15V + 6V + 10V2 + -4V2 = 27 + -6V + 4V2 + -27 + 6V + -4V2 Combine like terms: -15V + 6V = -9V -27 + -9V + 10V2 + -4V2 = 27 + -6V + 4V2 + -27 + 6V + -4V2 Combine like terms: 10V2 + -4V2 = 6V2 -27 + -9V + 6V2 = 27 + -6V + 4V2 + -27 + 6V + -4V2 Reorder the terms: -27 + -9V + 6V2 = 27 + -27 + -6V + 6V + 4V2 + -4V2 Combine like terms: 27 + -27 = 0 -27 + -9V + 6V2 = 0 + -6V + 6V + 4V2 + -4V2 -27 + -9V + 6V2 = -6V + 6V + 4V2 + -4V2 Combine like terms: -6V + 6V = 0 -27 + -9V + 6V2 = 0 + 4V2 + -4V2 -27 + -9V + 6V2 = 4V2 + -4V2 Combine like terms: 4V2 + -4V2 = 0 -27 + -9V + 6V2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + -3V + 2V2) = 0 Factor a trinomial. 3((-3 + -2V)(3 + -1V)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2V)' equal to zero and attempt to solve: Simplifying -3 + -2V = 0 Solving -3 + -2V = 0 Move all terms containing V to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2V = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2V = 0 + 3 -2V = 0 + 3 Combine like terms: 0 + 3 = 3 -2V = 3 Divide each side by '-2'. V = -1.5 Simplifying V = -1.5Subproblem 2
Set the factor '(3 + -1V)' equal to zero and attempt to solve: Simplifying 3 + -1V = 0 Solving 3 + -1V = 0 Move all terms containing V to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1V = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1V = 0 + -3 -1V = 0 + -3 Combine like terms: 0 + -3 = -3 -1V = -3 Divide each side by '-1'. V = 3 Simplifying V = 3Solution
V = {-1.5, 3}
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