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Simplifying 33 + -24v + 4v2 = 0 Solving 33 + -24v + 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'. 8.25 + -6v + v2 = 0 Move the constant term to the right: Add '-8.25' to each side of the equation. 8.25 + -6v + -8.25 + v2 = 0 + -8.25 Reorder the terms: 8.25 + -8.25 + -6v + v2 = 0 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + -6v + v2 = 0 + -8.25 -6v + v2 = 0 + -8.25 Combine like terms: 0 + -8.25 = -8.25 -6v + v2 = -8.25 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 = -8.25 + 9 Reorder the terms: 9 + -6v + v2 = -8.25 + 9 Combine like terms: -8.25 + 9 = 0.75 9 + -6v + v2 = 0.75 Factor a perfect square on the left side: (v + -3)(v + -3) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (v + -3) equal to 0.866025404 and -0.866025404.Subproblem 1
v + -3 = 0.866025404 Simplifying v + -3 = 0.866025404 Reorder the terms: -3 + v = 0.866025404 Solving -3 + v = 0.866025404 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 = 0.866025404 + 3 Combine like terms: -3 + 3 = 0 0 + v = 0.866025404 + 3 v = 0.866025404 + 3 Combine like terms: 0.866025404 + 3 = 3.866025404 v = 3.866025404 Simplifying v = 3.866025404Subproblem 2
v + -3 = -0.866025404 Simplifying v + -3 = -0.866025404 Reorder the terms: -3 + v = -0.866025404 Solving -3 + v = -0.866025404 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 = -0.866025404 + 3 Combine like terms: -3 + 3 = 0 0 + v = -0.866025404 + 3 v = -0.866025404 + 3 Combine like terms: -0.866025404 + 3 = 2.133974596 v = 2.133974596 Simplifying v = 2.133974596Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.866025404, 2.133974596}
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