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Simplifying v2 + 6v + -95 = 0 Reorder the terms: -95 + 6v + v2 = 0 Solving -95 + 6v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + 6v + 95 + v2 = 0 + 95 Reorder the terms: -95 + 95 + 6v + v2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 6v + v2 = 0 + 95 6v + v2 = 0 + 95 Combine like terms: 0 + 95 = 95 6v + v2 = 95 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 = 95 + 9 Reorder the terms: 9 + 6v + v2 = 95 + 9 Combine like terms: 95 + 9 = 104 9 + 6v + v2 = 104 Factor a perfect square on the left side: (v + 3)(v + 3) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (v + 3) equal to 10.198039027 and -10.198039027.Subproblem 1
v + 3 = 10.198039027 Simplifying v + 3 = 10.198039027 Reorder the terms: 3 + v = 10.198039027 Solving 3 + v = 10.198039027 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 = 10.198039027 + -3 Combine like terms: 3 + -3 = 0 0 + v = 10.198039027 + -3 v = 10.198039027 + -3 Combine like terms: 10.198039027 + -3 = 7.198039027 v = 7.198039027 Simplifying v = 7.198039027Subproblem 2
v + 3 = -10.198039027 Simplifying v + 3 = -10.198039027 Reorder the terms: 3 + v = -10.198039027 Solving 3 + v = -10.198039027 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 = -10.198039027 + -3 Combine like terms: 3 + -3 = 0 0 + v = -10.198039027 + -3 v = -10.198039027 + -3 Combine like terms: -10.198039027 + -3 = -13.198039027 v = -13.198039027 Simplifying v = -13.198039027Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.198039027, -13.198039027}
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