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Simplifying 7v2 + -6v + 1 = 0 Reorder the terms: 1 + -6v + 7v2 = 0 Solving 1 + -6v + 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'. 0.1428571429 + -0.8571428571v + v2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.8571428571v + -0.1428571429 + v2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -0.8571428571v + v2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -0.8571428571v + v2 = 0 + -0.1428571429 -0.8571428571v + v2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -0.8571428571v + v2 = -0.1428571429 The v term is -0.8571428571v. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571v + 0.1836734694 + v2 = -0.1428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571v + v2 = -0.1428571429 + 0.1836734694 Combine like terms: -0.1428571429 + 0.1836734694 = 0.0408163265 0.1836734694 + -0.8571428571v + v2 = 0.0408163265 Factor a perfect square on the left side: (v + -0.4285714286)(v + -0.4285714286) = 0.0408163265 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (v + -0.4285714286) equal to 0.202030509 and -0.202030509.Subproblem 1
v + -0.4285714286 = 0.202030509 Simplifying v + -0.4285714286 = 0.202030509 Reorder the terms: -0.4285714286 + v = 0.202030509 Solving -0.4285714286 + v = 0.202030509 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + v = 0.202030509 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + v = 0.202030509 + 0.4285714286 v = 0.202030509 + 0.4285714286 Combine like terms: 0.202030509 + 0.4285714286 = 0.6306019376 v = 0.6306019376 Simplifying v = 0.6306019376Subproblem 2
v + -0.4285714286 = -0.202030509 Simplifying v + -0.4285714286 = -0.202030509 Reorder the terms: -0.4285714286 + v = -0.202030509 Solving -0.4285714286 + v = -0.202030509 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + v = -0.202030509 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + v = -0.202030509 + 0.4285714286 v = -0.202030509 + 0.4285714286 Combine like terms: -0.202030509 + 0.4285714286 = 0.2265409196 v = 0.2265409196 Simplifying v = 0.2265409196Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.6306019376, 0.2265409196}
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