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Simplifying (7v + 8) + (v2 + 8v + 1) = 0 Reorder the terms: (8 + 7v) + (v2 + 8v + 1) = 0 Remove parenthesis around (8 + 7v) 8 + 7v + (v2 + 8v + 1) = 0 Reorder the terms: 8 + 7v + (1 + 8v + v2) = 0 Remove parenthesis around (1 + 8v + v2) 8 + 7v + 1 + 8v + v2 = 0 Reorder the terms: 8 + 1 + 7v + 8v + v2 = 0 Combine like terms: 8 + 1 = 9 9 + 7v + 8v + v2 = 0 Combine like terms: 7v + 8v = 15v 9 + 15v + v2 = 0 Solving 9 + 15v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 15v + -9 + v2 = 0 + -9 Reorder the terms: 9 + -9 + 15v + v2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 15v + v2 = 0 + -9 15v + v2 = 0 + -9 Combine like terms: 0 + -9 = -9 15v + v2 = -9 The v term is 15v. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15v + 56.25 + v2 = -9 + 56.25 Reorder the terms: 56.25 + 15v + v2 = -9 + 56.25 Combine like terms: -9 + 56.25 = 47.25 56.25 + 15v + v2 = 47.25 Factor a perfect square on the left side: (v + 7.5)(v + 7.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (v + 7.5) equal to 6.873863542 and -6.873863542.Subproblem 1
v + 7.5 = 6.873863542 Simplifying v + 7.5 = 6.873863542 Reorder the terms: 7.5 + v = 6.873863542 Solving 7.5 + v = 6.873863542 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + v = 6.873863542 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = 6.873863542 + -7.5 v = 6.873863542 + -7.5 Combine like terms: 6.873863542 + -7.5 = -0.626136458 v = -0.626136458 Simplifying v = -0.626136458Subproblem 2
v + 7.5 = -6.873863542 Simplifying v + 7.5 = -6.873863542 Reorder the terms: 7.5 + v = -6.873863542 Solving 7.5 + v = -6.873863542 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + v = -6.873863542 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = -6.873863542 + -7.5 v = -6.873863542 + -7.5 Combine like terms: -6.873863542 + -7.5 = -14.373863542 v = -14.373863542 Simplifying v = -14.373863542Solution
The solution to the problem is based on the solutions from the subproblems. v = {-0.626136458, -14.373863542}
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