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Simplifying v2 + 14v + -39 = 0 Reorder the terms: -39 + 14v + v2 = 0 Solving -39 + 14v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 14v + 39 + v2 = 0 + 39 Reorder the terms: -39 + 39 + 14v + v2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 14v + v2 = 0 + 39 14v + v2 = 0 + 39 Combine like terms: 0 + 39 = 39 14v + v2 = 39 The v term is 14v. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14v + 49 + v2 = 39 + 49 Reorder the terms: 49 + 14v + v2 = 39 + 49 Combine like terms: 39 + 49 = 88 49 + 14v + v2 = 88 Factor a perfect square on the left side: (v + 7)(v + 7) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (v + 7) equal to 9.38083152 and -9.38083152.Subproblem 1
v + 7 = 9.38083152 Simplifying v + 7 = 9.38083152 Reorder the terms: 7 + v = 9.38083152 Solving 7 + v = 9.38083152 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 9.38083152 + -7 Combine like terms: 7 + -7 = 0 0 + v = 9.38083152 + -7 v = 9.38083152 + -7 Combine like terms: 9.38083152 + -7 = 2.38083152 v = 2.38083152 Simplifying v = 2.38083152Subproblem 2
v + 7 = -9.38083152 Simplifying v + 7 = -9.38083152 Reorder the terms: 7 + v = -9.38083152 Solving 7 + v = -9.38083152 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = -9.38083152 + -7 Combine like terms: 7 + -7 = 0 0 + v = -9.38083152 + -7 v = -9.38083152 + -7 Combine like terms: -9.38083152 + -7 = -16.38083152 v = -16.38083152 Simplifying v = -16.38083152Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.38083152, -16.38083152}
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