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Simplifying v2 + -2v + -62 = 0 Reorder the terms: -62 + -2v + v2 = 0 Solving -62 + -2v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + -2v + 62 + v2 = 0 + 62 Reorder the terms: -62 + 62 + -2v + v2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -2v + v2 = 0 + 62 -2v + v2 = 0 + 62 Combine like terms: 0 + 62 = 62 -2v + v2 = 62 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 = 62 + 1 Reorder the terms: 1 + -2v + v2 = 62 + 1 Combine like terms: 62 + 1 = 63 1 + -2v + v2 = 63 Factor a perfect square on the left side: (v + -1)(v + -1) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (v + -1) equal to 7.937253933 and -7.937253933.Subproblem 1
v + -1 = 7.937253933 Simplifying v + -1 = 7.937253933 Reorder the terms: -1 + v = 7.937253933 Solving -1 + v = 7.937253933 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 = 7.937253933 + 1 Combine like terms: -1 + 1 = 0 0 + v = 7.937253933 + 1 v = 7.937253933 + 1 Combine like terms: 7.937253933 + 1 = 8.937253933 v = 8.937253933 Simplifying v = 8.937253933Subproblem 2
v + -1 = -7.937253933 Simplifying v + -1 = -7.937253933 Reorder the terms: -1 + v = -7.937253933 Solving -1 + v = -7.937253933 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 = -7.937253933 + 1 Combine like terms: -1 + 1 = 0 0 + v = -7.937253933 + 1 v = -7.937253933 + 1 Combine like terms: -7.937253933 + 1 = -6.937253933 v = -6.937253933 Simplifying v = -6.937253933Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.937253933, -6.937253933}
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