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Simplifying 4v2 + 32v + -9 = 0 Reorder the terms: -9 + 32v + 4v2 = 0 Solving -9 + 32v + 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'. -2.25 + 8v + v2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 8v + 2.25 + v2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 8v + v2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 8v + v2 = 0 + 2.25 8v + v2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 8v + v2 = 2.25 The v term is 8v. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8v + 16 + v2 = 2.25 + 16 Reorder the terms: 16 + 8v + v2 = 2.25 + 16 Combine like terms: 2.25 + 16 = 18.25 16 + 8v + v2 = 18.25 Factor a perfect square on the left side: (v + 4)(v + 4) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (v + 4) equal to 4.272001873 and -4.272001873.Subproblem 1
v + 4 = 4.272001873 Simplifying v + 4 = 4.272001873 Reorder the terms: 4 + v = 4.272001873 Solving 4 + v = 4.272001873 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 4.272001873 + -4 Combine like terms: 4 + -4 = 0 0 + v = 4.272001873 + -4 v = 4.272001873 + -4 Combine like terms: 4.272001873 + -4 = 0.272001873 v = 0.272001873 Simplifying v = 0.272001873Subproblem 2
v + 4 = -4.272001873 Simplifying v + 4 = -4.272001873 Reorder the terms: 4 + v = -4.272001873 Solving 4 + v = -4.272001873 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = -4.272001873 + -4 Combine like terms: 4 + -4 = 0 0 + v = -4.272001873 + -4 v = -4.272001873 + -4 Combine like terms: -4.272001873 + -4 = -8.272001873 v = -8.272001873 Simplifying v = -8.272001873Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.272001873, -8.272001873}
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