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Simplifying 8v + -11 = v2 + -2v + -4v + 8 Reorder the terms: -11 + 8v = v2 + -2v + -4v + 8 Reorder the terms: -11 + 8v = 8 + -2v + -4v + v2 Combine like terms: -2v + -4v = -6v -11 + 8v = 8 + -6v + v2 Solving -11 + 8v = 8 + -6v + v2 Solving for variable 'v'. Reorder the terms: -11 + -8 + 8v + 6v + -1v2 = 8 + -6v + v2 + -8 + 6v + -1v2 Combine like terms: -11 + -8 = -19 -19 + 8v + 6v + -1v2 = 8 + -6v + v2 + -8 + 6v + -1v2 Combine like terms: 8v + 6v = 14v -19 + 14v + -1v2 = 8 + -6v + v2 + -8 + 6v + -1v2 Reorder the terms: -19 + 14v + -1v2 = 8 + -8 + -6v + 6v + v2 + -1v2 Combine like terms: 8 + -8 = 0 -19 + 14v + -1v2 = 0 + -6v + 6v + v2 + -1v2 -19 + 14v + -1v2 = -6v + 6v + v2 + -1v2 Combine like terms: -6v + 6v = 0 -19 + 14v + -1v2 = 0 + v2 + -1v2 -19 + 14v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -19 + 14v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 19 + -14v + v2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + -14v + -19 + v2 = 0 + -19 Reorder the terms: 19 + -19 + -14v + v2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -14v + v2 = 0 + -19 -14v + v2 = 0 + -19 Combine like terms: 0 + -19 = -19 -14v + v2 = -19 The v term is -14v. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14v + 49 + v2 = -19 + 49 Reorder the terms: 49 + -14v + v2 = -19 + 49 Combine like terms: -19 + 49 = 30 49 + -14v + v2 = 30 Factor a perfect square on the left side: (v + -7)(v + -7) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (v + -7) equal to 5.477225575 and -5.477225575.Subproblem 1
v + -7 = 5.477225575 Simplifying v + -7 = 5.477225575 Reorder the terms: -7 + v = 5.477225575 Solving -7 + v = 5.477225575 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v = 5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + v = 5.477225575 + 7 v = 5.477225575 + 7 Combine like terms: 5.477225575 + 7 = 12.477225575 v = 12.477225575 Simplifying v = 12.477225575Subproblem 2
v + -7 = -5.477225575 Simplifying v + -7 = -5.477225575 Reorder the terms: -7 + v = -5.477225575 Solving -7 + v = -5.477225575 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + v = -5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + v = -5.477225575 + 7 v = -5.477225575 + 7 Combine like terms: -5.477225575 + 7 = 1.522774425 v = 1.522774425 Simplifying v = 1.522774425Solution
The solution to the problem is based on the solutions from the subproblems. v = {12.477225575, 1.522774425}
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