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Simplifying 81 + -36v + -4v2 = 0 Solving 81 + -36v + -4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -20.25 + 9v + v2 = 0 Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + 9v + 20.25 + v2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + 9v + v2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + 9v + v2 = 0 + 20.25 9v + v2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 9v + v2 = 20.25 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 = 20.25 + 20.25 Reorder the terms: 20.25 + 9v + v2 = 20.25 + 20.25 Combine like terms: 20.25 + 20.25 = 40.5 20.25 + 9v + v2 = 40.5 Factor a perfect square on the left side: (v + 4.5)(v + 4.5) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (v + 4.5) equal to 6.363961031 and -6.363961031.Subproblem 1
v + 4.5 = 6.363961031 Simplifying v + 4.5 = 6.363961031 Reorder the terms: 4.5 + v = 6.363961031 Solving 4.5 + v = 6.363961031 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 = 6.363961031 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = 6.363961031 + -4.5 v = 6.363961031 + -4.5 Combine like terms: 6.363961031 + -4.5 = 1.863961031 v = 1.863961031 Simplifying v = 1.863961031Subproblem 2
v + 4.5 = -6.363961031 Simplifying v + 4.5 = -6.363961031 Reorder the terms: 4.5 + v = -6.363961031 Solving 4.5 + v = -6.363961031 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 = -6.363961031 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + v = -6.363961031 + -4.5 v = -6.363961031 + -4.5 Combine like terms: -6.363961031 + -4.5 = -10.863961031 v = -10.863961031 Simplifying v = -10.863961031Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.863961031, -10.863961031}
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