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Simplifying 3v2 + 36v + 49 = 0 Reorder the terms: 49 + 36v + 3v2 = 0 Solving 49 + 36v + 3v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 16.33333333 + 12v + v2 = 0 Move the constant term to the right: Add '-16.33333333' to each side of the equation. 16.33333333 + 12v + -16.33333333 + v2 = 0 + -16.33333333 Reorder the terms: 16.33333333 + -16.33333333 + 12v + v2 = 0 + -16.33333333 Combine like terms: 16.33333333 + -16.33333333 = 0.00000000 0.00000000 + 12v + v2 = 0 + -16.33333333 12v + v2 = 0 + -16.33333333 Combine like terms: 0 + -16.33333333 = -16.33333333 12v + v2 = -16.33333333 The v term is 12v. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12v + 36 + v2 = -16.33333333 + 36 Reorder the terms: 36 + 12v + v2 = -16.33333333 + 36 Combine like terms: -16.33333333 + 36 = 19.66666667 36 + 12v + v2 = 19.66666667 Factor a perfect square on the left side: (v + 6)(v + 6) = 19.66666667 Calculate the square root of the right side: 4.434711566 Break this problem into two subproblems by setting (v + 6) equal to 4.434711566 and -4.434711566.Subproblem 1
v + 6 = 4.434711566 Simplifying v + 6 = 4.434711566 Reorder the terms: 6 + v = 4.434711566 Solving 6 + v = 4.434711566 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = 4.434711566 + -6 Combine like terms: 6 + -6 = 0 0 + v = 4.434711566 + -6 v = 4.434711566 + -6 Combine like terms: 4.434711566 + -6 = -1.565288434 v = -1.565288434 Simplifying v = -1.565288434Subproblem 2
v + 6 = -4.434711566 Simplifying v + 6 = -4.434711566 Reorder the terms: 6 + v = -4.434711566 Solving 6 + v = -4.434711566 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = -4.434711566 + -6 Combine like terms: 6 + -6 = 0 0 + v = -4.434711566 + -6 v = -4.434711566 + -6 Combine like terms: -4.434711566 + -6 = -10.434711566 v = -10.434711566 Simplifying v = -10.434711566Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.565288434, -10.434711566}
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