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Simplifying -1v2 + 6v + -7 = 0 Reorder the terms: -7 + 6v + -1v2 = 0 Solving -7 + 6v + -1v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -6v + v2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6v + -7 + v2 = 0 + -7 Reorder the terms: 7 + -7 + -6v + v2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6v + v2 = 0 + -7 -6v + v2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6v + v2 = -7 The v term is -6v. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6v + 9 + v2 = -7 + 9 Reorder the terms: 9 + -6v + v2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6v + v2 = 2 Factor a perfect square on the left side: (v + -3)(v + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (v + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
v + -3 = 1.414213562 Simplifying v + -3 = 1.414213562 Reorder the terms: -3 + v = 1.414213562 Solving -3 + v = 1.414213562 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + v = 1.414213562 + 3 v = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 v = 4.414213562 Simplifying v = 4.414213562Subproblem 2
v + -3 = -1.414213562 Simplifying v + -3 = -1.414213562 Reorder the terms: -3 + v = -1.414213562 Solving -3 + v = -1.414213562 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + v = -1.414213562 + 3 v = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 v = 1.585786438 Simplifying v = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.414213562, 1.585786438}
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