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Simplifying 4v2 + -24v + -5 = 0 Reorder the terms: -5 + -24v + 4v2 = 0 Solving -5 + -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'. -1.25 + -6v + v2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -6v + 1.25 + v2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -6v + v2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -6v + v2 = 0 + 1.25 -6v + v2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -6v + v2 = 1.25 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 = 1.25 + 9 Reorder the terms: 9 + -6v + v2 = 1.25 + 9 Combine like terms: 1.25 + 9 = 10.25 9 + -6v + v2 = 10.25 Factor a perfect square on the left side: (v + -3)(v + -3) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (v + -3) equal to 3.201562119 and -3.201562119.Subproblem 1
v + -3 = 3.201562119 Simplifying v + -3 = 3.201562119 Reorder the terms: -3 + v = 3.201562119 Solving -3 + v = 3.201562119 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 = 3.201562119 + 3 Combine like terms: -3 + 3 = 0 0 + v = 3.201562119 + 3 v = 3.201562119 + 3 Combine like terms: 3.201562119 + 3 = 6.201562119 v = 6.201562119 Simplifying v = 6.201562119Subproblem 2
v + -3 = -3.201562119 Simplifying v + -3 = -3.201562119 Reorder the terms: -3 + v = -3.201562119 Solving -3 + v = -3.201562119 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 = -3.201562119 + 3 Combine like terms: -3 + 3 = 0 0 + v = -3.201562119 + 3 v = -3.201562119 + 3 Combine like terms: -3.201562119 + 3 = -0.201562119 v = -0.201562119 Simplifying v = -0.201562119Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.201562119, -0.201562119}
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