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Simplifying (v + 6)(v + 6) = 20 Reorder the terms: (6 + v)(v + 6) = 20 Reorder the terms: (6 + v)(6 + v) = 20 Multiply (6 + v) * (6 + v) (6(6 + v) + v(6 + v)) = 20 ((6 * 6 + v * 6) + v(6 + v)) = 20 ((36 + 6v) + v(6 + v)) = 20 (36 + 6v + (6 * v + v * v)) = 20 (36 + 6v + (6v + v2)) = 20 Combine like terms: 6v + 6v = 12v (36 + 12v + v2) = 20 Solving 36 + 12v + v2 = 20 Solving for variable 'v'. Reorder the terms: 36 + -20 + 12v + v2 = 20 + -20 Combine like terms: 36 + -20 = 16 16 + 12v + v2 = 20 + -20 Combine like terms: 20 + -20 = 0 16 + 12v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 12v + -16 + v2 = 0 + -16 Reorder the terms: 16 + -16 + 12v + v2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 12v + v2 = 0 + -16 12v + v2 = 0 + -16 Combine like terms: 0 + -16 = -16 12v + v2 = -16 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 + 36 Reorder the terms: 36 + 12v + v2 = -16 + 36 Combine like terms: -16 + 36 = 20 36 + 12v + v2 = 20 Factor a perfect square on the left side: (v + 6)(v + 6) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (v + 6) equal to 4.472135955 and -4.472135955.Subproblem 1
v + 6 = 4.472135955 Simplifying v + 6 = 4.472135955 Reorder the terms: 6 + v = 4.472135955 Solving 6 + v = 4.472135955 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 = 4.472135955 + -6 Combine like terms: 6 + -6 = 0 0 + v = 4.472135955 + -6 v = 4.472135955 + -6 Combine like terms: 4.472135955 + -6 = -1.527864045 v = -1.527864045 Simplifying v = -1.527864045Subproblem 2
v + 6 = -4.472135955 Simplifying v + 6 = -4.472135955 Reorder the terms: 6 + v = -4.472135955 Solving 6 + v = -4.472135955 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 = -4.472135955 + -6 Combine like terms: 6 + -6 = 0 0 + v = -4.472135955 + -6 v = -4.472135955 + -6 Combine like terms: -4.472135955 + -6 = -10.472135955 v = -10.472135955 Simplifying v = -10.472135955Solution
The solution to the problem is based on the solutions from the subproblems. v = {-1.527864045, -10.472135955}
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