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Simplifying v2 + 4v + 7v = 28 Reorder the terms: 4v + 7v + v2 = 28 Combine like terms: 4v + 7v = 11v 11v + v2 = 28 Solving 11v + v2 = 28 Solving for variable 'v'. Reorder the terms: -28 + 11v + v2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 11v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 11v + 28 + v2 = 0 + 28 Reorder the terms: -28 + 28 + 11v + v2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 11v + v2 = 0 + 28 11v + v2 = 0 + 28 Combine like terms: 0 + 28 = 28 11v + v2 = 28 The v term is 11v. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11v + 30.25 + v2 = 28 + 30.25 Reorder the terms: 30.25 + 11v + v2 = 28 + 30.25 Combine like terms: 28 + 30.25 = 58.25 30.25 + 11v + v2 = 58.25 Factor a perfect square on the left side: (v + 5.5)(v + 5.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (v + 5.5) equal to 7.632168761 and -7.632168761.Subproblem 1
v + 5.5 = 7.632168761 Simplifying v + 5.5 = 7.632168761 Reorder the terms: 5.5 + v = 7.632168761 Solving 5.5 + v = 7.632168761 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + v = 7.632168761 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + v = 7.632168761 + -5.5 v = 7.632168761 + -5.5 Combine like terms: 7.632168761 + -5.5 = 2.132168761 v = 2.132168761 Simplifying v = 2.132168761Subproblem 2
v + 5.5 = -7.632168761 Simplifying v + 5.5 = -7.632168761 Reorder the terms: 5.5 + v = -7.632168761 Solving 5.5 + v = -7.632168761 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + v = -7.632168761 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + v = -7.632168761 + -5.5 v = -7.632168761 + -5.5 Combine like terms: -7.632168761 + -5.5 = -13.132168761 v = -13.132168761 Simplifying v = -13.132168761Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.132168761, -13.132168761}
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