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Simplifying 7v2 + -7v + -4 = 0 Reorder the terms: -4 + -7v + 7v2 = 0 Solving -4 + -7v + 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'. -0.5714285714 + -1v + v2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -1v + 0.5714285714 + v2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -1v + v2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -1v + v2 = 0 + 0.5714285714 -1v + v2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -1v + v2 = 0.5714285714 The v term is -1v. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1v + 0.25 + v2 = 0.5714285714 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 0.5714285714 + 0.25 Combine like terms: 0.5714285714 + 0.25 = 0.8214285714 0.25 + -1v + v2 = 0.8214285714 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 0.8214285714 Calculate the square root of the right side: 0.906326967 Break this problem into two subproblems by setting (v + -0.5) equal to 0.906326967 and -0.906326967.Subproblem 1
v + -0.5 = 0.906326967 Simplifying v + -0.5 = 0.906326967 Reorder the terms: -0.5 + v = 0.906326967 Solving -0.5 + v = 0.906326967 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 0.906326967 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 0.906326967 + 0.5 v = 0.906326967 + 0.5 Combine like terms: 0.906326967 + 0.5 = 1.406326967 v = 1.406326967 Simplifying v = 1.406326967Subproblem 2
v + -0.5 = -0.906326967 Simplifying v + -0.5 = -0.906326967 Reorder the terms: -0.5 + v = -0.906326967 Solving -0.5 + v = -0.906326967 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -0.906326967 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -0.906326967 + 0.5 v = -0.906326967 + 0.5 Combine like terms: -0.906326967 + 0.5 = -0.406326967 v = -0.406326967 Simplifying v = -0.406326967Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.406326967, -0.406326967}
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