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Simplifying 4V3 + -80V2 + 160V = 0 Reorder the terms: 160V + -80V2 + 4V3 = 0 Solving 160V + -80V2 + 4V3 = 0 Solving for variable 'V'. Factor out the Greatest Common Factor (GCF), '4V'. 4V(40 + -20V + V2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'V' equal to zero and attempt to solve: Simplifying V = 0 Solving V = 0 Move all terms containing V to the left, all other terms to the right. Simplifying V = 0Subproblem 2
Set the factor '(40 + -20V + V2)' equal to zero and attempt to solve: Simplifying 40 + -20V + V2 = 0 Solving 40 + -20V + V2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -20V + -40 + V2 = 0 + -40 Reorder the terms: 40 + -40 + -20V + V2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -20V + V2 = 0 + -40 -20V + V2 = 0 + -40 Combine like terms: 0 + -40 = -40 -20V + V2 = -40 The V term is -20V. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20V + 100 + V2 = -40 + 100 Reorder the terms: 100 + -20V + V2 = -40 + 100 Combine like terms: -40 + 100 = 60 100 + -20V + V2 = 60 Factor a perfect square on the left side: (V + -10)(V + -10) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (V + -10) equal to 7.745966692 and -7.745966692.Subproblem 1
V + -10 = 7.745966692 Simplifying V + -10 = 7.745966692 Reorder the terms: -10 + V = 7.745966692 Solving -10 + V = 7.745966692 Solving for variable 'V'. Move all terms containing V to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + V = 7.745966692 + 10 Combine like terms: -10 + 10 = 0 0 + V = 7.745966692 + 10 V = 7.745966692 + 10 Combine like terms: 7.745966692 + 10 = 17.745966692 V = 17.745966692 Simplifying V = 17.745966692Subproblem 2
V + -10 = -7.745966692 Simplifying V + -10 = -7.745966692 Reorder the terms: -10 + V = -7.745966692 Solving -10 + V = -7.745966692 Solving for variable 'V'. Move all terms containing V to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + V = -7.745966692 + 10 Combine like terms: -10 + 10 = 0 0 + V = -7.745966692 + 10 V = -7.745966692 + 10 Combine like terms: -7.745966692 + 10 = 2.254033308 V = 2.254033308 Simplifying V = 2.254033308Solution
The solution to the problem is based on the solutions from the subproblems. V = {17.745966692, 2.254033308}Solution
V = {0, 17.745966692, 2.254033308}
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