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Simplifying v2 + 6.6v + -51.48 = 0 Reorder the terms: -51.48 + 6.6v + v2 = 0 Solving -51.48 + 6.6v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '51.48' to each side of the equation. -51.48 + 6.6v + 51.48 + v2 = 0 + 51.48 Reorder the terms: -51.48 + 51.48 + 6.6v + v2 = 0 + 51.48 Combine like terms: -51.48 + 51.48 = 0.00 0.00 + 6.6v + v2 = 0 + 51.48 6.6v + v2 = 0 + 51.48 Combine like terms: 0 + 51.48 = 51.48 6.6v + v2 = 51.48 The v term is 6.6v. Take half its coefficient (3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. 6.6v + 10.89 + v2 = 51.48 + 10.89 Reorder the terms: 10.89 + 6.6v + v2 = 51.48 + 10.89 Combine like terms: 51.48 + 10.89 = 62.37 10.89 + 6.6v + v2 = 62.37 Factor a perfect square on the left side: (v + 3.3)(v + 3.3) = 62.37 Calculate the square root of the right side: 7.897467949 Break this problem into two subproblems by setting (v + 3.3) equal to 7.897467949 and -7.897467949.Subproblem 1
v + 3.3 = 7.897467949 Simplifying v + 3.3 = 7.897467949 Reorder the terms: 3.3 + v = 7.897467949 Solving 3.3 + v = 7.897467949 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + v = 7.897467949 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + v = 7.897467949 + -3.3 v = 7.897467949 + -3.3 Combine like terms: 7.897467949 + -3.3 = 4.597467949 v = 4.597467949 Simplifying v = 4.597467949Subproblem 2
v + 3.3 = -7.897467949 Simplifying v + 3.3 = -7.897467949 Reorder the terms: 3.3 + v = -7.897467949 Solving 3.3 + v = -7.897467949 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + v = -7.897467949 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + v = -7.897467949 + -3.3 v = -7.897467949 + -3.3 Combine like terms: -7.897467949 + -3.3 = -11.197467949 v = -11.197467949 Simplifying v = -11.197467949Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.597467949, -11.197467949}
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