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Simplifying -1v2 + -2v + 30 = 0 Reorder the terms: 30 + -2v + -1v2 = 0 Solving 30 + -2v + -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'. -30 + 2v + v2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 2v + 30 + v2 = 0 + 30 Reorder the terms: -30 + 30 + 2v + v2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 2v + v2 = 0 + 30 2v + v2 = 0 + 30 Combine like terms: 0 + 30 = 30 2v + v2 = 30 The v term is 2v. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2v + 1 + v2 = 30 + 1 Reorder the terms: 1 + 2v + v2 = 30 + 1 Combine like terms: 30 + 1 = 31 1 + 2v + v2 = 31 Factor a perfect square on the left side: (v + 1)(v + 1) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (v + 1) equal to 5.567764363 and -5.567764363.Subproblem 1
v + 1 = 5.567764363 Simplifying v + 1 = 5.567764363 Reorder the terms: 1 + v = 5.567764363 Solving 1 + v = 5.567764363 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + v = 5.567764363 + -1 v = 5.567764363 + -1 Combine like terms: 5.567764363 + -1 = 4.567764363 v = 4.567764363 Simplifying v = 4.567764363Subproblem 2
v + 1 = -5.567764363 Simplifying v + 1 = -5.567764363 Reorder the terms: 1 + v = -5.567764363 Solving 1 + v = -5.567764363 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + v = -5.567764363 + -1 v = -5.567764363 + -1 Combine like terms: -5.567764363 + -1 = -6.567764363 v = -6.567764363 Simplifying v = -6.567764363Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.567764363, -6.567764363}
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