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Simplifying 6V2 + -17V + -15 = 0 Reorder the terms: -15 + -17V + 6V2 = 0 Solving -15 + -17V + 6V2 = 0 Solving for variable 'V'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + -2.833333333V + V2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2.833333333V + 2.5 + V2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2.833333333V + V2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2.833333333V + V2 = 0 + 2.5 -2.833333333V + V2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2.833333333V + V2 = 2.5 The V term is -2.833333333V. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333V + 2.006944445 + V2 = 2.5 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333V + V2 = 2.5 + 2.006944445 Combine like terms: 2.5 + 2.006944445 = 4.506944445 2.006944445 + -2.833333333V + V2 = 4.506944445 Factor a perfect square on the left side: (V + -1.416666667)(V + -1.416666667) = 4.506944445 Calculate the square root of the right side: 2.122956534 Break this problem into two subproblems by setting (V + -1.416666667) equal to 2.122956534 and -2.122956534.Subproblem 1
V + -1.416666667 = 2.122956534 Simplifying V + -1.416666667 = 2.122956534 Reorder the terms: -1.416666667 + V = 2.122956534 Solving -1.416666667 + V = 2.122956534 Solving for variable 'V'. Move all terms containing V to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + V = 2.122956534 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + V = 2.122956534 + 1.416666667 V = 2.122956534 + 1.416666667 Combine like terms: 2.122956534 + 1.416666667 = 3.539623201 V = 3.539623201 Simplifying V = 3.539623201Subproblem 2
V + -1.416666667 = -2.122956534 Simplifying V + -1.416666667 = -2.122956534 Reorder the terms: -1.416666667 + V = -2.122956534 Solving -1.416666667 + V = -2.122956534 Solving for variable 'V'. Move all terms containing V to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + V = -2.122956534 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + V = -2.122956534 + 1.416666667 V = -2.122956534 + 1.416666667 Combine like terms: -2.122956534 + 1.416666667 = -0.706289867 V = -0.706289867 Simplifying V = -0.706289867Solution
The solution to the problem is based on the solutions from the subproblems. V = {3.539623201, -0.706289867}
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