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Simplifying v2 + 12v + 26 = 0 Reorder the terms: 26 + 12v + v2 = 0 Solving 26 + 12v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 12v + -26 + v2 = 0 + -26 Reorder the terms: 26 + -26 + 12v + v2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 12v + v2 = 0 + -26 12v + v2 = 0 + -26 Combine like terms: 0 + -26 = -26 12v + v2 = -26 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 = -26 + 36 Reorder the terms: 36 + 12v + v2 = -26 + 36 Combine like terms: -26 + 36 = 10 36 + 12v + v2 = 10 Factor a perfect square on the left side: (v + 6)(v + 6) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (v + 6) equal to 3.16227766 and -3.16227766.Subproblem 1
v + 6 = 3.16227766 Simplifying v + 6 = 3.16227766 Reorder the terms: 6 + v = 3.16227766 Solving 6 + v = 3.16227766 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 = 3.16227766 + -6 Combine like terms: 6 + -6 = 0 0 + v = 3.16227766 + -6 v = 3.16227766 + -6 Combine like terms: 3.16227766 + -6 = -2.83772234 v = -2.83772234 Simplifying v = -2.83772234Subproblem 2
v + 6 = -3.16227766 Simplifying v + 6 = -3.16227766 Reorder the terms: 6 + v = -3.16227766 Solving 6 + v = -3.16227766 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 = -3.16227766 + -6 Combine like terms: 6 + -6 = 0 0 + v = -3.16227766 + -6 v = -3.16227766 + -6 Combine like terms: -3.16227766 + -6 = -9.16227766 v = -9.16227766 Simplifying v = -9.16227766Solution
The solution to the problem is based on the solutions from the subproblems. v = {-2.83772234, -9.16227766}
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