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Simplifying 3v2 + 36v + 49 = 84 Reorder the terms: 49 + 36v + 3v2 = 84 Solving 49 + 36v + 3v2 = 84 Solving for variable 'v'. Reorder the terms: 49 + -84 + 36v + 3v2 = 84 + -84 Combine like terms: 49 + -84 = -35 -35 + 36v + 3v2 = 84 + -84 Combine like terms: 84 + -84 = 0 -35 + 36v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.66666667 + 12v + v2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + 12v + 11.66666667 + v2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + 12v + v2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + 12v + v2 = 0 + 11.66666667 12v + v2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 12v + v2 = 11.66666667 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 = 11.66666667 + 36 Reorder the terms: 36 + 12v + v2 = 11.66666667 + 36 Combine like terms: 11.66666667 + 36 = 47.66666667 36 + 12v + v2 = 47.66666667 Factor a perfect square on the left side: (v + 6)(v + 6) = 47.66666667 Calculate the square root of the right side: 6.904105059 Break this problem into two subproblems by setting (v + 6) equal to 6.904105059 and -6.904105059.Subproblem 1
v + 6 = 6.904105059 Simplifying v + 6 = 6.904105059 Reorder the terms: 6 + v = 6.904105059 Solving 6 + v = 6.904105059 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 = 6.904105059 + -6 Combine like terms: 6 + -6 = 0 0 + v = 6.904105059 + -6 v = 6.904105059 + -6 Combine like terms: 6.904105059 + -6 = 0.904105059 v = 0.904105059 Simplifying v = 0.904105059Subproblem 2
v + 6 = -6.904105059 Simplifying v + 6 = -6.904105059 Reorder the terms: 6 + v = -6.904105059 Solving 6 + v = -6.904105059 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 = -6.904105059 + -6 Combine like terms: 6 + -6 = 0 0 + v = -6.904105059 + -6 v = -6.904105059 + -6 Combine like terms: -6.904105059 + -6 = -12.904105059 v = -12.904105059 Simplifying v = -12.904105059Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.904105059, -12.904105059}
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