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Simplifying (6v2 + -2v + -7) + (v2 + -3v + 4) = 0 Reorder the terms: (-7 + -2v + 6v2) + (v2 + -3v + 4) = 0 Remove parenthesis around (-7 + -2v + 6v2) -7 + -2v + 6v2 + (v2 + -3v + 4) = 0 Reorder the terms: -7 + -2v + 6v2 + (4 + -3v + v2) = 0 Remove parenthesis around (4 + -3v + v2) -7 + -2v + 6v2 + 4 + -3v + v2 = 0 Reorder the terms: -7 + 4 + -2v + -3v + 6v2 + v2 = 0 Combine like terms: -7 + 4 = -3 -3 + -2v + -3v + 6v2 + v2 = 0 Combine like terms: -2v + -3v = -5v -3 + -5v + 6v2 + v2 = 0 Combine like terms: 6v2 + v2 = 7v2 -3 + -5v + 7v2 = 0 Solving -3 + -5v + 7v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -0.7142857143v + v2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.7142857143v + 0.4285714286 + v2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.7142857143v + v2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.7142857143v + v2 = 0 + 0.4285714286 -0.7142857143v + v2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.7142857143v + v2 = 0.4285714286 The v term is -0.7142857143v. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143v + 0.1275510204 + v2 = 0.4285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143v + v2 = 0.4285714286 + 0.1275510204 Combine like terms: 0.4285714286 + 0.1275510204 = 0.556122449 0.1275510204 + -0.7142857143v + v2 = 0.556122449 Factor a perfect square on the left side: (v + -0.3571428572)(v + -0.3571428572) = 0.556122449 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (v + -0.3571428572) equal to 0.745736179 and -0.745736179.Subproblem 1
v + -0.3571428572 = 0.745736179 Simplifying v + -0.3571428572 = 0.745736179 Reorder the terms: -0.3571428572 + v = 0.745736179 Solving -0.3571428572 + v = 0.745736179 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + v = 0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + v = 0.745736179 + 0.3571428572 v = 0.745736179 + 0.3571428572 Combine like terms: 0.745736179 + 0.3571428572 = 1.1028790362 v = 1.1028790362 Simplifying v = 1.1028790362Subproblem 2
v + -0.3571428572 = -0.745736179 Simplifying v + -0.3571428572 = -0.745736179 Reorder the terms: -0.3571428572 + v = -0.745736179 Solving -0.3571428572 + v = -0.745736179 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + v = -0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + v = -0.745736179 + 0.3571428572 v = -0.745736179 + 0.3571428572 Combine like terms: -0.745736179 + 0.3571428572 = -0.3885933218 v = -0.3885933218 Simplifying v = -0.3885933218Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.1028790362, -0.3885933218}
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