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Simplifying v2 + -2v + -33 = 0 Reorder the terms: -33 + -2v + v2 = 0 Solving -33 + -2v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -2v + 33 + v2 = 0 + 33 Reorder the terms: -33 + 33 + -2v + v2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -2v + v2 = 0 + 33 -2v + v2 = 0 + 33 Combine like terms: 0 + 33 = 33 -2v + v2 = 33 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 = 33 + 1 Reorder the terms: 1 + -2v + v2 = 33 + 1 Combine like terms: 33 + 1 = 34 1 + -2v + v2 = 34 Factor a perfect square on the left side: (v + -1)(v + -1) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (v + -1) equal to 5.830951895 and -5.830951895.Subproblem 1
v + -1 = 5.830951895 Simplifying v + -1 = 5.830951895 Reorder the terms: -1 + v = 5.830951895 Solving -1 + v = 5.830951895 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 = 5.830951895 + 1 Combine like terms: -1 + 1 = 0 0 + v = 5.830951895 + 1 v = 5.830951895 + 1 Combine like terms: 5.830951895 + 1 = 6.830951895 v = 6.830951895 Simplifying v = 6.830951895Subproblem 2
v + -1 = -5.830951895 Simplifying v + -1 = -5.830951895 Reorder the terms: -1 + v = -5.830951895 Solving -1 + v = -5.830951895 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 = -5.830951895 + 1 Combine like terms: -1 + 1 = 0 0 + v = -5.830951895 + 1 v = -5.830951895 + 1 Combine like terms: -5.830951895 + 1 = -4.830951895 v = -4.830951895 Simplifying v = -4.830951895Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.830951895, -4.830951895}
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