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Simplifying 7v2 + -10v = 11 Reorder the terms: -10v + 7v2 = 11 Solving -10v + 7v2 = 11 Solving for variable 'v'. Reorder the terms: -11 + -10v + 7v2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -10v + 7v2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.571428571 + -1.428571429v + v2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + -1.428571429v + 1.571428571 + v2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + -1.428571429v + v2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + -1.428571429v + v2 = 0 + 1.571428571 -1.428571429v + v2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 -1.428571429v + v2 = 1.571428571 The v term is -1.428571429v. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429v + 0.5102040819 + v2 = 1.571428571 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429v + v2 = 1.571428571 + 0.5102040819 Combine like terms: 1.571428571 + 0.5102040819 = 2.0816326529 0.5102040819 + -1.428571429v + v2 = 2.0816326529 Factor a perfect square on the left side: (v + -0.7142857145)(v + -0.7142857145) = 2.0816326529 Calculate the square root of the right side: 1.44278642 Break this problem into two subproblems by setting (v + -0.7142857145) equal to 1.44278642 and -1.44278642.Subproblem 1
v + -0.7142857145 = 1.44278642 Simplifying v + -0.7142857145 = 1.44278642 Reorder the terms: -0.7142857145 + v = 1.44278642 Solving -0.7142857145 + v = 1.44278642 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + v = 1.44278642 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + v = 1.44278642 + 0.7142857145 v = 1.44278642 + 0.7142857145 Combine like terms: 1.44278642 + 0.7142857145 = 2.1570721345 v = 2.1570721345 Simplifying v = 2.1570721345Subproblem 2
v + -0.7142857145 = -1.44278642 Simplifying v + -0.7142857145 = -1.44278642 Reorder the terms: -0.7142857145 + v = -1.44278642 Solving -0.7142857145 + v = -1.44278642 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + v = -1.44278642 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + v = -1.44278642 + 0.7142857145 v = -1.44278642 + 0.7142857145 Combine like terms: -1.44278642 + 0.7142857145 = -0.7285007055 v = -0.7285007055 Simplifying v = -0.7285007055Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.1570721345, -0.7285007055}
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