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Simplifying 2v2 + 9v + 5 = (v + 5) * 62 Reorder the terms: 5 + 9v + 2v2 = (v + 5) * 62 Reorder the terms: 5 + 9v + 2v2 = (5 + v) * 62 Reorder the terms for easier multiplication: 5 + 9v + 2v2 = 62(5 + v) 5 + 9v + 2v2 = (5 * 62 + v * 62) 5 + 9v + 2v2 = (310 + 62v) Solving 5 + 9v + 2v2 = 310 + 62v Solving for variable 'v'. Reorder the terms: 5 + -310 + 9v + -62v + 2v2 = 310 + 62v + -310 + -62v Combine like terms: 5 + -310 = -305 -305 + 9v + -62v + 2v2 = 310 + 62v + -310 + -62v Combine like terms: 9v + -62v = -53v -305 + -53v + 2v2 = 310 + 62v + -310 + -62v Reorder the terms: -305 + -53v + 2v2 = 310 + -310 + 62v + -62v Combine like terms: 310 + -310 = 0 -305 + -53v + 2v2 = 0 + 62v + -62v -305 + -53v + 2v2 = 62v + -62v Combine like terms: 62v + -62v = 0 -305 + -53v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -152.5 + -26.5v + v2 = 0 Move the constant term to the right: Add '152.5' to each side of the equation. -152.5 + -26.5v + 152.5 + v2 = 0 + 152.5 Reorder the terms: -152.5 + 152.5 + -26.5v + v2 = 0 + 152.5 Combine like terms: -152.5 + 152.5 = 0.0 0.0 + -26.5v + v2 = 0 + 152.5 -26.5v + v2 = 0 + 152.5 Combine like terms: 0 + 152.5 = 152.5 -26.5v + v2 = 152.5 The v term is -26.5v. Take half its coefficient (-13.25). Square it (175.5625) and add it to both sides. Add '175.5625' to each side of the equation. -26.5v + 175.5625 + v2 = 152.5 + 175.5625 Reorder the terms: 175.5625 + -26.5v + v2 = 152.5 + 175.5625 Combine like terms: 152.5 + 175.5625 = 328.0625 175.5625 + -26.5v + v2 = 328.0625 Factor a perfect square on the left side: (v + -13.25)(v + -13.25) = 328.0625 Calculate the square root of the right side: 18.112495687 Break this problem into two subproblems by setting (v + -13.25) equal to 18.112495687 and -18.112495687.Subproblem 1
v + -13.25 = 18.112495687 Simplifying v + -13.25 = 18.112495687 Reorder the terms: -13.25 + v = 18.112495687 Solving -13.25 + v = 18.112495687 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13.25' to each side of the equation. -13.25 + 13.25 + v = 18.112495687 + 13.25 Combine like terms: -13.25 + 13.25 = 0.00 0.00 + v = 18.112495687 + 13.25 v = 18.112495687 + 13.25 Combine like terms: 18.112495687 + 13.25 = 31.362495687 v = 31.362495687 Simplifying v = 31.362495687Subproblem 2
v + -13.25 = -18.112495687 Simplifying v + -13.25 = -18.112495687 Reorder the terms: -13.25 + v = -18.112495687 Solving -13.25 + v = -18.112495687 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13.25' to each side of the equation. -13.25 + 13.25 + v = -18.112495687 + 13.25 Combine like terms: -13.25 + 13.25 = 0.00 0.00 + v = -18.112495687 + 13.25 v = -18.112495687 + 13.25 Combine like terms: -18.112495687 + 13.25 = -4.862495687 v = -4.862495687 Simplifying v = -4.862495687Solution
The solution to the problem is based on the solutions from the subproblems. v = {31.362495687, -4.862495687}
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