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Simplifying 16v2 + 49v + 36 = 0 Reorder the terms: 36 + 49v + 16v2 = 0 Solving 36 + 49v + 16v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.25 + 3.0625v + v2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 3.0625v + -2.25 + v2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 3.0625v + v2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 3.0625v + v2 = 0 + -2.25 3.0625v + v2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 3.0625v + v2 = -2.25 The v term is 3.0625v. Take half its coefficient (1.53125). Square it (2.344726563) and add it to both sides. Add '2.344726563' to each side of the equation. 3.0625v + 2.344726563 + v2 = -2.25 + 2.344726563 Reorder the terms: 2.344726563 + 3.0625v + v2 = -2.25 + 2.344726563 Combine like terms: -2.25 + 2.344726563 = 0.094726563 2.344726563 + 3.0625v + v2 = 0.094726563 Factor a perfect square on the left side: (v + 1.53125)(v + 1.53125) = 0.094726563 Calculate the square root of the right side: 0.307776807 Break this problem into two subproblems by setting (v + 1.53125) equal to 0.307776807 and -0.307776807.Subproblem 1
v + 1.53125 = 0.307776807 Simplifying v + 1.53125 = 0.307776807 Reorder the terms: 1.53125 + v = 0.307776807 Solving 1.53125 + v = 0.307776807 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.53125' to each side of the equation. 1.53125 + -1.53125 + v = 0.307776807 + -1.53125 Combine like terms: 1.53125 + -1.53125 = 0.00000 0.00000 + v = 0.307776807 + -1.53125 v = 0.307776807 + -1.53125 Combine like terms: 0.307776807 + -1.53125 = -1.223473193 v = -1.223473193 Simplifying v = -1.223473193Subproblem 2
v + 1.53125 = -0.307776807 Simplifying v + 1.53125 = -0.307776807 Reorder the terms: 1.53125 + v = -0.307776807 Solving 1.53125 + v = -0.307776807 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.53125' to each side of the equation. 1.53125 + -1.53125 + v = -0.307776807 + -1.53125 Combine like terms: 1.53125 + -1.53125 = 0.00000 0.00000 + v = -0.307776807 + -1.53125 v = -0.307776807 + -1.53125 Combine like terms: -0.307776807 + -1.53125 = -1.839026807 v = -1.839026807 Simplifying v = -1.839026807Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.223473193, -1.839026807}
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