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Simplifying 7v2 + 2v + -21 = 0 Reorder the terms: -21 + 2v + 7v2 = 0 Solving -21 + 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'. -3 + 0.2857142857v + v2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.2857142857v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + 0.2857142857v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.2857142857v + v2 = 0 + 3 0.2857142857v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.2857142857v + v2 = 3 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 = 3 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857v + v2 = 3 + 0.02040816328 Combine like terms: 3 + 0.02040816328 = 3.02040816328 0.02040816328 + 0.2857142857v + v2 = 3.02040816328 Factor a perfect square on the left side: (v + 0.1428571429)(v + 0.1428571429) = 3.02040816328 Calculate the square root of the right side: 1.737932152 Break this problem into two subproblems by setting (v + 0.1428571429) equal to 1.737932152 and -1.737932152.Subproblem 1
v + 0.1428571429 = 1.737932152 Simplifying v + 0.1428571429 = 1.737932152 Reorder the terms: 0.1428571429 + v = 1.737932152 Solving 0.1428571429 + v = 1.737932152 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 = 1.737932152 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + v = 1.737932152 + -0.1428571429 v = 1.737932152 + -0.1428571429 Combine like terms: 1.737932152 + -0.1428571429 = 1.5950750091 v = 1.5950750091 Simplifying v = 1.5950750091Subproblem 2
v + 0.1428571429 = -1.737932152 Simplifying v + 0.1428571429 = -1.737932152 Reorder the terms: 0.1428571429 + v = -1.737932152 Solving 0.1428571429 + v = -1.737932152 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 = -1.737932152 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + v = -1.737932152 + -0.1428571429 v = -1.737932152 + -0.1428571429 Combine like terms: -1.737932152 + -0.1428571429 = -1.8807892949 v = -1.8807892949 Simplifying v = -1.8807892949Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.5950750091, -1.8807892949}
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