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Simplifying (6v2 + -1v + -4) + (2v2 + -5v + 3) = 0 Reorder the terms: (-4 + -1v + 6v2) + (2v2 + -5v + 3) = 0 Remove parenthesis around (-4 + -1v + 6v2) -4 + -1v + 6v2 + (2v2 + -5v + 3) = 0 Reorder the terms: -4 + -1v + 6v2 + (3 + -5v + 2v2) = 0 Remove parenthesis around (3 + -5v + 2v2) -4 + -1v + 6v2 + 3 + -5v + 2v2 = 0 Reorder the terms: -4 + 3 + -1v + -5v + 6v2 + 2v2 = 0 Combine like terms: -4 + 3 = -1 -1 + -1v + -5v + 6v2 + 2v2 = 0 Combine like terms: -1v + -5v = -6v -1 + -6v + 6v2 + 2v2 = 0 Combine like terms: 6v2 + 2v2 = 8v2 -1 + -6v + 8v2 = 0 Solving -1 + -6v + 8v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.75v + v2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.75v + 0.125 + v2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.75v + v2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.75v + v2 = 0 + 0.125 -0.75v + v2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.75v + v2 = 0.125 The v term is -0.75v. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75v + 0.140625 + v2 = 0.125 + 0.140625 Reorder the terms: 0.140625 + -0.75v + v2 = 0.125 + 0.140625 Combine like terms: 0.125 + 0.140625 = 0.265625 0.140625 + -0.75v + v2 = 0.265625 Factor a perfect square on the left side: (v + -0.375)(v + -0.375) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (v + -0.375) equal to 0.515388203 and -0.515388203.Subproblem 1
v + -0.375 = 0.515388203 Simplifying v + -0.375 = 0.515388203 Reorder the terms: -0.375 + v = 0.515388203 Solving -0.375 + v = 0.515388203 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + v = 0.515388203 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + v = 0.515388203 + 0.375 v = 0.515388203 + 0.375 Combine like terms: 0.515388203 + 0.375 = 0.890388203 v = 0.890388203 Simplifying v = 0.890388203Subproblem 2
v + -0.375 = -0.515388203 Simplifying v + -0.375 = -0.515388203 Reorder the terms: -0.375 + v = -0.515388203 Solving -0.375 + v = -0.515388203 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + v = -0.515388203 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + v = -0.515388203 + 0.375 v = -0.515388203 + 0.375 Combine like terms: -0.515388203 + 0.375 = -0.140388203 v = -0.140388203 Simplifying v = -0.140388203Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.890388203, -0.140388203}
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