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Simplifying 11v2 + 12v = 4 Reorder the terms: 12v + 11v2 = 4 Solving 12v + 11v2 = 4 Solving for variable 'v'. Reorder the terms: -4 + 12v + 11v2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 12v + 11v2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + 1.090909091v + v2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + 1.090909091v + 0.3636363636 + v2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + 1.090909091v + v2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + 1.090909091v + v2 = 0 + 0.3636363636 1.090909091v + v2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 1.090909091v + v2 = 0.3636363636 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 = 0.3636363636 + 0.2975206612 Reorder the terms: 0.2975206612 + 1.090909091v + v2 = 0.3636363636 + 0.2975206612 Combine like terms: 0.3636363636 + 0.2975206612 = 0.6611570248 0.2975206612 + 1.090909091v + v2 = 0.6611570248 Factor a perfect square on the left side: (v + 0.5454545455)(v + 0.5454545455) = 0.6611570248 Calculate the square root of the right side: 0.813115628 Break this problem into two subproblems by setting (v + 0.5454545455) equal to 0.813115628 and -0.813115628.Subproblem 1
v + 0.5454545455 = 0.813115628 Simplifying v + 0.5454545455 = 0.813115628 Reorder the terms: 0.5454545455 + v = 0.813115628 Solving 0.5454545455 + v = 0.813115628 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 = 0.813115628 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + v = 0.813115628 + -0.5454545455 v = 0.813115628 + -0.5454545455 Combine like terms: 0.813115628 + -0.5454545455 = 0.2676610825 v = 0.2676610825 Simplifying v = 0.2676610825Subproblem 2
v + 0.5454545455 = -0.813115628 Simplifying v + 0.5454545455 = -0.813115628 Reorder the terms: 0.5454545455 + v = -0.813115628 Solving 0.5454545455 + v = -0.813115628 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 = -0.813115628 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + v = -0.813115628 + -0.5454545455 v = -0.813115628 + -0.5454545455 Combine like terms: -0.813115628 + -0.5454545455 = -1.3585701735 v = -1.3585701735 Simplifying v = -1.3585701735Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.2676610825, -1.3585701735}
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