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Simplifying 4v2 + -1v + -44 = 8 Reorder the terms: -44 + -1v + 4v2 = 8 Solving -44 + -1v + 4v2 = 8 Solving for variable 'v'. Reorder the terms: -44 + -8 + -1v + 4v2 = 8 + -8 Combine like terms: -44 + -8 = -52 -52 + -1v + 4v2 = 8 + -8 Combine like terms: 8 + -8 = 0 -52 + -1v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13 + -0.25v + v2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -0.25v + 13 + v2 = 0 + 13 Reorder the terms: -13 + 13 + -0.25v + v2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -0.25v + v2 = 0 + 13 -0.25v + v2 = 0 + 13 Combine like terms: 0 + 13 = 13 -0.25v + v2 = 13 The v term is -0.25v. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25v + 0.015625 + v2 = 13 + 0.015625 Reorder the terms: 0.015625 + -0.25v + v2 = 13 + 0.015625 Combine like terms: 13 + 0.015625 = 13.015625 0.015625 + -0.25v + v2 = 13.015625 Factor a perfect square on the left side: (v + -0.125)(v + -0.125) = 13.015625 Calculate the square root of the right side: 3.607717422 Break this problem into two subproblems by setting (v + -0.125) equal to 3.607717422 and -3.607717422.Subproblem 1
v + -0.125 = 3.607717422 Simplifying v + -0.125 = 3.607717422 Reorder the terms: -0.125 + v = 3.607717422 Solving -0.125 + v = 3.607717422 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + v = 3.607717422 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + v = 3.607717422 + 0.125 v = 3.607717422 + 0.125 Combine like terms: 3.607717422 + 0.125 = 3.732717422 v = 3.732717422 Simplifying v = 3.732717422Subproblem 2
v + -0.125 = -3.607717422 Simplifying v + -0.125 = -3.607717422 Reorder the terms: -0.125 + v = -3.607717422 Solving -0.125 + v = -3.607717422 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + v = -3.607717422 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + v = -3.607717422 + 0.125 v = -3.607717422 + 0.125 Combine like terms: -3.607717422 + 0.125 = -3.482717422 v = -3.482717422 Simplifying v = -3.482717422Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.732717422, -3.482717422}
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