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Simplifying V2 + -4V = 13 Reorder the terms: -4V + V2 = 13 Solving -4V + V2 = 13 Solving for variable 'V'. Reorder the terms: -13 + -4V + V2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -4V + V2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -4V + 13 + V2 = 0 + 13 Reorder the terms: -13 + 13 + -4V + V2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4V + V2 = 0 + 13 -4V + V2 = 0 + 13 Combine like terms: 0 + 13 = 13 -4V + V2 = 13 The V term is -4V. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4V + 4 + V2 = 13 + 4 Reorder the terms: 4 + -4V + V2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + -4V + V2 = 17 Factor a perfect square on the left side: (V + -2)(V + -2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (V + -2) equal to 4.123105626 and -4.123105626.Subproblem 1
V + -2 = 4.123105626 Simplifying V + -2 = 4.123105626 Reorder the terms: -2 + V = 4.123105626 Solving -2 + V = 4.123105626 Solving for variable 'V'. Move all terms containing V to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + V = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + V = 4.123105626 + 2 V = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 V = 6.123105626 Simplifying V = 6.123105626Subproblem 2
V + -2 = -4.123105626 Simplifying V + -2 = -4.123105626 Reorder the terms: -2 + V = -4.123105626 Solving -2 + V = -4.123105626 Solving for variable 'V'. Move all terms containing V to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + V = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + V = -4.123105626 + 2 V = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 V = -2.123105626 Simplifying V = -2.123105626Solution
The solution to the problem is based on the solutions from the subproblems. V = {6.123105626, -2.123105626}
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