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Simplifying -5v2 + 24v + 41 = 0 Reorder the terms: 41 + 24v + -5v2 = 0 Solving 41 + 24v + -5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8.2 + -4.8v + v2 = 0 Move the constant term to the right: Add '8.2' to each side of the equation. -8.2 + -4.8v + 8.2 + v2 = 0 + 8.2 Reorder the terms: -8.2 + 8.2 + -4.8v + v2 = 0 + 8.2 Combine like terms: -8.2 + 8.2 = 0.0 0.0 + -4.8v + v2 = 0 + 8.2 -4.8v + v2 = 0 + 8.2 Combine like terms: 0 + 8.2 = 8.2 -4.8v + v2 = 8.2 The v term is -4.8v. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8v + 5.76 + v2 = 8.2 + 5.76 Reorder the terms: 5.76 + -4.8v + v2 = 8.2 + 5.76 Combine like terms: 8.2 + 5.76 = 13.96 5.76 + -4.8v + v2 = 13.96 Factor a perfect square on the left side: (v + -2.4)(v + -2.4) = 13.96 Calculate the square root of the right side: 3.736308338 Break this problem into two subproblems by setting (v + -2.4) equal to 3.736308338 and -3.736308338.Subproblem 1
v + -2.4 = 3.736308338 Simplifying v + -2.4 = 3.736308338 Reorder the terms: -2.4 + v = 3.736308338 Solving -2.4 + v = 3.736308338 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + v = 3.736308338 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + v = 3.736308338 + 2.4 v = 3.736308338 + 2.4 Combine like terms: 3.736308338 + 2.4 = 6.136308338 v = 6.136308338 Simplifying v = 6.136308338Subproblem 2
v + -2.4 = -3.736308338 Simplifying v + -2.4 = -3.736308338 Reorder the terms: -2.4 + v = -3.736308338 Solving -2.4 + v = -3.736308338 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + v = -3.736308338 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + v = -3.736308338 + 2.4 v = -3.736308338 + 2.4 Combine like terms: -3.736308338 + 2.4 = -1.336308338 v = -1.336308338 Simplifying v = -1.336308338Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.136308338, -1.336308338}
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