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Simplifying 0 = (-2v2 + 5v + -4) + (v2 + 3v + 7) Reorder the terms: 0 = (-4 + 5v + -2v2) + (v2 + 3v + 7) Remove parenthesis around (-4 + 5v + -2v2) 0 = -4 + 5v + -2v2 + (v2 + 3v + 7) Reorder the terms: 0 = -4 + 5v + -2v2 + (7 + 3v + v2) Remove parenthesis around (7 + 3v + v2) 0 = -4 + 5v + -2v2 + 7 + 3v + v2 Reorder the terms: 0 = -4 + 7 + 5v + 3v + -2v2 + v2 Combine like terms: -4 + 7 = 3 0 = 3 + 5v + 3v + -2v2 + v2 Combine like terms: 5v + 3v = 8v 0 = 3 + 8v + -2v2 + v2 Combine like terms: -2v2 + v2 = -1v2 0 = 3 + 8v + -1v2 Solving 0 = 3 + 8v + -1v2 Solving for variable 'v'. Combine like terms: 0 + -3 = -3 -3 + -8v + v2 = 3 + 8v + -1v2 + -3 + -8v + v2 Reorder the terms: -3 + -8v + v2 = 3 + -3 + 8v + -8v + -1v2 + v2 Combine like terms: 3 + -3 = 0 -3 + -8v + v2 = 0 + 8v + -8v + -1v2 + v2 -3 + -8v + v2 = 8v + -8v + -1v2 + v2 Combine like terms: 8v + -8v = 0 -3 + -8v + v2 = 0 + -1v2 + v2 -3 + -8v + v2 = -1v2 + v2 Combine like terms: -1v2 + v2 = 0 -3 + -8v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -8v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + -8v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8v + v2 = 0 + 3 -8v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 -8v + v2 = 3 The v term is -8v. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8v + 16 + v2 = 3 + 16 Reorder the terms: 16 + -8v + v2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + -8v + v2 = 19 Factor a perfect square on the left side: (v + -4)(v + -4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (v + -4) equal to 4.358898944 and -4.358898944.Subproblem 1
v + -4 = 4.358898944 Simplifying v + -4 = 4.358898944 Reorder the terms: -4 + v = 4.358898944 Solving -4 + v = 4.358898944 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + v = 4.358898944 + 4 v = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 v = 8.358898944 Simplifying v = 8.358898944Subproblem 2
v + -4 = -4.358898944 Simplifying v + -4 = -4.358898944 Reorder the terms: -4 + v = -4.358898944 Solving -4 + v = -4.358898944 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + v = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + v = -4.358898944 + 4 v = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 v = -0.358898944 Simplifying v = -0.358898944Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.358898944, -0.358898944}
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