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Simplifying 3V2 + -3V = 80 Reorder the terms: -3V + 3V2 = 80 Solving -3V + 3V2 = 80 Solving for variable 'V'. Reorder the terms: -80 + -3V + 3V2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -3V + 3V2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -26.66666667 + -1V + V2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + -1V + 26.66666667 + V2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + -1V + V2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + -1V + V2 = 0 + 26.66666667 -1V + V2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 -1V + V2 = 26.66666667 The V term is -1V. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1V + 0.25 + V2 = 26.66666667 + 0.25 Reorder the terms: 0.25 + -1V + V2 = 26.66666667 + 0.25 Combine like terms: 26.66666667 + 0.25 = 26.91666667 0.25 + -1V + V2 = 26.91666667 Factor a perfect square on the left side: (V + -0.5)(V + -0.5) = 26.91666667 Calculate the square root of the right side: 5.188127472 Break this problem into two subproblems by setting (V + -0.5) equal to 5.188127472 and -5.188127472.Subproblem 1
V + -0.5 = 5.188127472 Simplifying V + -0.5 = 5.188127472 Reorder the terms: -0.5 + V = 5.188127472 Solving -0.5 + V = 5.188127472 Solving for variable 'V'. Move all terms containing V to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + V = 5.188127472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + V = 5.188127472 + 0.5 V = 5.188127472 + 0.5 Combine like terms: 5.188127472 + 0.5 = 5.688127472 V = 5.688127472 Simplifying V = 5.688127472Subproblem 2
V + -0.5 = -5.188127472 Simplifying V + -0.5 = -5.188127472 Reorder the terms: -0.5 + V = -5.188127472 Solving -0.5 + V = -5.188127472 Solving for variable 'V'. Move all terms containing V to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + V = -5.188127472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + V = -5.188127472 + 0.5 V = -5.188127472 + 0.5 Combine like terms: -5.188127472 + 0.5 = -4.688127472 V = -4.688127472 Simplifying V = -4.688127472Solution
The solution to the problem is based on the solutions from the subproblems. V = {5.688127472, -4.688127472}
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