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Simplifying (9v2 + 9v) + -1(-2v2 + -3v + 8) = 0 Reorder the terms: (9v + 9v2) + -1(-2v2 + -3v + 8) = 0 Remove parenthesis around (9v + 9v2) 9v + 9v2 + -1(-2v2 + -3v + 8) = 0 Reorder the terms: 9v + 9v2 + -1(8 + -3v + -2v2) = 0 9v + 9v2 + (8 * -1 + -3v * -1 + -2v2 * -1) = 0 9v + 9v2 + (-8 + 3v + 2v2) = 0 Reorder the terms: -8 + 9v + 3v + 9v2 + 2v2 = 0 Combine like terms: 9v + 3v = 12v -8 + 12v + 9v2 + 2v2 = 0 Combine like terms: 9v2 + 2v2 = 11v2 -8 + 12v + 11v2 = 0 Solving -8 + 12v + 11v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.7272727273 + 1.090909091v + v2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + 1.090909091v + 0.7272727273 + v2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + 1.090909091v + v2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + 1.090909091v + v2 = 0 + 0.7272727273 1.090909091v + v2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 1.090909091v + v2 = 0.7272727273 The v term is 1.090909091v. Take half its coefficient (0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. 1.090909091v + 0.2975206612 + v2 = 0.7272727273 + 0.2975206612 Reorder the terms: 0.2975206612 + 1.090909091v + v2 = 0.7272727273 + 0.2975206612 Combine like terms: 0.7272727273 + 0.2975206612 = 1.0247933885 0.2975206612 + 1.090909091v + v2 = 1.0247933885 Factor a perfect square on the left side: (v + 0.5454545455)(v + 0.5454545455) = 1.0247933885 Calculate the square root of the right side: 1.012320793 Break this problem into two subproblems by setting (v + 0.5454545455) equal to 1.012320793 and -1.012320793.Subproblem 1
v + 0.5454545455 = 1.012320793 Simplifying v + 0.5454545455 = 1.012320793 Reorder the terms: 0.5454545455 + v = 1.012320793 Solving 0.5454545455 + v = 1.012320793 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + v = 1.012320793 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + v = 1.012320793 + -0.5454545455 v = 1.012320793 + -0.5454545455 Combine like terms: 1.012320793 + -0.5454545455 = 0.4668662475 v = 0.4668662475 Simplifying v = 0.4668662475Subproblem 2
v + 0.5454545455 = -1.012320793 Simplifying v + 0.5454545455 = -1.012320793 Reorder the terms: 0.5454545455 + v = -1.012320793 Solving 0.5454545455 + v = -1.012320793 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5454545455' to each side of the equation. 0.5454545455 + -0.5454545455 + v = -1.012320793 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + v = -1.012320793 + -0.5454545455 v = -1.012320793 + -0.5454545455 Combine like terms: -1.012320793 + -0.5454545455 = -1.5577753385 v = -1.5577753385 Simplifying v = -1.5577753385Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.4668662475, -1.5577753385}
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