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Simplifying v2 + 9v + 6 = 8 Reorder the terms: 6 + 9v + v2 = 8 Solving 6 + 9v + v2 = 8 Solving for variable 'v'. Reorder the terms: 6 + -8 + 9v + v2 = 8 + -8 Combine like terms: 6 + -8 = -2 -2 + 9v + v2 = 8 + -8 Combine like terms: 8 + -8 = 0 -2 + 9v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 9v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + 9v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 9v + v2 = 0 + 2 9v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 9v + v2 = 2 The v term is 9v. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9v + 20.25 + v2 = 2 + 20.25 Reorder the terms: 20.25 + 9v + v2 = 2 + 20.25 Combine like terms: 2 + 20.25 = 22.25 20.25 + 9v + v2 = 22.25 Factor a perfect square on the left side: (v + 4.5)(v + 4.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (v + 4.5) equal to 4.716990566 and -4.716990566.Subproblem 1
v + 4.5 = 4.716990566 Simplifying v + 4.5 = 4.716990566 Reorder the terms: 4.5 + v = 4.716990566 Solving 4.5 + v = 4.716990566 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + v = 4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = 4.716990566 + -4.5 v = 4.716990566 + -4.5 Combine like terms: 4.716990566 + -4.5 = 0.216990566 v = 0.216990566 Simplifying v = 0.216990566Subproblem 2
v + 4.5 = -4.716990566 Simplifying v + 4.5 = -4.716990566 Reorder the terms: 4.5 + v = -4.716990566 Solving 4.5 + v = -4.716990566 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + v = -4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = -4.716990566 + -4.5 v = -4.716990566 + -4.5 Combine like terms: -4.716990566 + -4.5 = -9.216990566 v = -9.216990566 Simplifying v = -9.216990566Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.216990566, -9.216990566}
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