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Simplifying 7v2 + 2v + -45 = 0 Reorder the terms: -45 + 2v + 7v2 = 0 Solving -45 + 2v + 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'. -6.428571429 + 0.2857142857v + v2 = 0 Move the constant term to the right: Add '6.428571429' to each side of the equation. -6.428571429 + 0.2857142857v + 6.428571429 + v2 = 0 + 6.428571429 Reorder the terms: -6.428571429 + 6.428571429 + 0.2857142857v + v2 = 0 + 6.428571429 Combine like terms: -6.428571429 + 6.428571429 = 0.000000000 0.000000000 + 0.2857142857v + v2 = 0 + 6.428571429 0.2857142857v + v2 = 0 + 6.428571429 Combine like terms: 0 + 6.428571429 = 6.428571429 0.2857142857v + v2 = 6.428571429 The v term is 0.2857142857v. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857v + 0.02040816328 + v2 = 6.428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857v + v2 = 6.428571429 + 0.02040816328 Combine like terms: 6.428571429 + 0.02040816328 = 6.44897959228 0.02040816328 + 0.2857142857v + v2 = 6.44897959228 Factor a perfect square on the left side: (v + 0.1428571429)(v + 0.1428571429) = 6.44897959228 Calculate the square root of the right side: 2.539484119 Break this problem into two subproblems by setting (v + 0.1428571429) equal to 2.539484119 and -2.539484119.Subproblem 1
v + 0.1428571429 = 2.539484119 Simplifying v + 0.1428571429 = 2.539484119 Reorder the terms: 0.1428571429 + v = 2.539484119 Solving 0.1428571429 + v = 2.539484119 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + v = 2.539484119 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + v = 2.539484119 + -0.1428571429 v = 2.539484119 + -0.1428571429 Combine like terms: 2.539484119 + -0.1428571429 = 2.3966269761 v = 2.3966269761 Simplifying v = 2.3966269761Subproblem 2
v + 0.1428571429 = -2.539484119 Simplifying v + 0.1428571429 = -2.539484119 Reorder the terms: 0.1428571429 + v = -2.539484119 Solving 0.1428571429 + v = -2.539484119 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + v = -2.539484119 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + v = -2.539484119 + -0.1428571429 v = -2.539484119 + -0.1428571429 Combine like terms: -2.539484119 + -0.1428571429 = -2.6823412619 v = -2.6823412619 Simplifying v = -2.6823412619Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.3966269761, -2.6823412619}
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