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Simplifying v2 + 4v + -56 = 0 Reorder the terms: -56 + 4v + v2 = 0 Solving -56 + 4v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 4v + 56 + v2 = 0 + 56 Reorder the terms: -56 + 56 + 4v + v2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 4v + v2 = 0 + 56 4v + v2 = 0 + 56 Combine like terms: 0 + 56 = 56 4v + v2 = 56 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = 56 + 4 Reorder the terms: 4 + 4v + v2 = 56 + 4 Combine like terms: 56 + 4 = 60 4 + 4v + v2 = 60 Factor a perfect square on the left side: (v + 2)(v + 2) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (v + 2) equal to 7.745966692 and -7.745966692.Subproblem 1
v + 2 = 7.745966692 Simplifying v + 2 = 7.745966692 Reorder the terms: 2 + v = 7.745966692 Solving 2 + v = 7.745966692 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 7.745966692 + -2 Combine like terms: 2 + -2 = 0 0 + v = 7.745966692 + -2 v = 7.745966692 + -2 Combine like terms: 7.745966692 + -2 = 5.745966692 v = 5.745966692 Simplifying v = 5.745966692Subproblem 2
v + 2 = -7.745966692 Simplifying v + 2 = -7.745966692 Reorder the terms: 2 + v = -7.745966692 Solving 2 + v = -7.745966692 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = -7.745966692 + -2 Combine like terms: 2 + -2 = 0 0 + v = -7.745966692 + -2 v = -7.745966692 + -2 Combine like terms: -7.745966692 + -2 = -9.745966692 v = -9.745966692 Simplifying v = -9.745966692Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.745966692, -9.745966692}
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