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Simplifying v2 + 44v + -6600 = 0 Reorder the terms: -6600 + 44v + v2 = 0 Solving -6600 + 44v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '6600' to each side of the equation. -6600 + 44v + 6600 + v2 = 0 + 6600 Reorder the terms: -6600 + 6600 + 44v + v2 = 0 + 6600 Combine like terms: -6600 + 6600 = 0 0 + 44v + v2 = 0 + 6600 44v + v2 = 0 + 6600 Combine like terms: 0 + 6600 = 6600 44v + v2 = 6600 The v term is 44v. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44v + 484 + v2 = 6600 + 484 Reorder the terms: 484 + 44v + v2 = 6600 + 484 Combine like terms: 6600 + 484 = 7084 484 + 44v + v2 = 7084 Factor a perfect square on the left side: (v + 22)(v + 22) = 7084 Calculate the square root of the right side: 84.16650165 Break this problem into two subproblems by setting (v + 22) equal to 84.16650165 and -84.16650165.Subproblem 1
v + 22 = 84.16650165 Simplifying v + 22 = 84.16650165 Reorder the terms: 22 + v = 84.16650165 Solving 22 + v = 84.16650165 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + v = 84.16650165 + -22 Combine like terms: 22 + -22 = 0 0 + v = 84.16650165 + -22 v = 84.16650165 + -22 Combine like terms: 84.16650165 + -22 = 62.16650165 v = 62.16650165 Simplifying v = 62.16650165Subproblem 2
v + 22 = -84.16650165 Simplifying v + 22 = -84.16650165 Reorder the terms: 22 + v = -84.16650165 Solving 22 + v = -84.16650165 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + v = -84.16650165 + -22 Combine like terms: 22 + -22 = 0 0 + v = -84.16650165 + -22 v = -84.16650165 + -22 Combine like terms: -84.16650165 + -22 = -106.16650165 v = -106.16650165 Simplifying v = -106.16650165Solution
The solution to the problem is based on the solutions from the subproblems. v = {62.16650165, -106.16650165}
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