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Simplifying v2 + -6v = 42 Reorder the terms: -6v + v2 = 42 Solving -6v + v2 = 42 Solving for variable 'v'. Reorder the terms: -42 + -6v + v2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + -6v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -6v + 42 + v2 = 0 + 42 Reorder the terms: -42 + 42 + -6v + v2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -6v + v2 = 0 + 42 -6v + v2 = 0 + 42 Combine like terms: 0 + 42 = 42 -6v + v2 = 42 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 = 42 + 9 Reorder the terms: 9 + -6v + v2 = 42 + 9 Combine like terms: 42 + 9 = 51 9 + -6v + v2 = 51 Factor a perfect square on the left side: (v + -3)(v + -3) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (v + -3) equal to 7.141428429 and -7.141428429.Subproblem 1
v + -3 = 7.141428429 Simplifying v + -3 = 7.141428429 Reorder the terms: -3 + v = 7.141428429 Solving -3 + v = 7.141428429 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 = 7.141428429 + 3 Combine like terms: -3 + 3 = 0 0 + v = 7.141428429 + 3 v = 7.141428429 + 3 Combine like terms: 7.141428429 + 3 = 10.141428429 v = 10.141428429 Simplifying v = 10.141428429Subproblem 2
v + -3 = -7.141428429 Simplifying v + -3 = -7.141428429 Reorder the terms: -3 + v = -7.141428429 Solving -3 + v = -7.141428429 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 = -7.141428429 + 3 Combine like terms: -3 + 3 = 0 0 + v = -7.141428429 + 3 v = -7.141428429 + 3 Combine like terms: -7.141428429 + 3 = -4.141428429 v = -4.141428429 Simplifying v = -4.141428429Solution
The solution to the problem is based on the solutions from the subproblems. v = {10.141428429, -4.141428429}
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