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Simplifying v2 + 14v = 41 Reorder the terms: 14v + v2 = 41 Solving 14v + v2 = 41 Solving for variable 'v'. Reorder the terms: -41 + 14v + v2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + 14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 14v + 41 + v2 = 0 + 41 Reorder the terms: -41 + 41 + 14v + v2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 14v + v2 = 0 + 41 14v + v2 = 0 + 41 Combine like terms: 0 + 41 = 41 14v + v2 = 41 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 = 41 + 49 Reorder the terms: 49 + 14v + v2 = 41 + 49 Combine like terms: 41 + 49 = 90 49 + 14v + v2 = 90 Factor a perfect square on the left side: (v + 7)(v + 7) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (v + 7) equal to 9.486832981 and -9.486832981.Subproblem 1
v + 7 = 9.486832981 Simplifying v + 7 = 9.486832981 Reorder the terms: 7 + v = 9.486832981 Solving 7 + v = 9.486832981 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 = 9.486832981 + -7 Combine like terms: 7 + -7 = 0 0 + v = 9.486832981 + -7 v = 9.486832981 + -7 Combine like terms: 9.486832981 + -7 = 2.486832981 v = 2.486832981 Simplifying v = 2.486832981Subproblem 2
v + 7 = -9.486832981 Simplifying v + 7 = -9.486832981 Reorder the terms: 7 + v = -9.486832981 Solving 7 + v = -9.486832981 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 = -9.486832981 + -7 Combine like terms: 7 + -7 = 0 0 + v = -9.486832981 + -7 v = -9.486832981 + -7 Combine like terms: -9.486832981 + -7 = -16.486832981 v = -16.486832981 Simplifying v = -16.486832981Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.486832981, -16.486832981}
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