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Simplifying (-5v2 + 6v + -2) + (3v2 + 7v + 4) = 0 Reorder the terms: (-2 + 6v + -5v2) + (3v2 + 7v + 4) = 0 Remove parenthesis around (-2 + 6v + -5v2) -2 + 6v + -5v2 + (3v2 + 7v + 4) = 0 Reorder the terms: -2 + 6v + -5v2 + (4 + 7v + 3v2) = 0 Remove parenthesis around (4 + 7v + 3v2) -2 + 6v + -5v2 + 4 + 7v + 3v2 = 0 Reorder the terms: -2 + 4 + 6v + 7v + -5v2 + 3v2 = 0 Combine like terms: -2 + 4 = 2 2 + 6v + 7v + -5v2 + 3v2 = 0 Combine like terms: 6v + 7v = 13v 2 + 13v + -5v2 + 3v2 = 0 Combine like terms: -5v2 + 3v2 = -2v2 2 + 13v + -2v2 = 0 Solving 2 + 13v + -2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + -6.5v + v2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.5v + 1 + v2 = 0 + 1 Reorder the terms: -1 + 1 + -6.5v + v2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.5v + v2 = 0 + 1 -6.5v + v2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.5v + v2 = 1 The v term is -6.5v. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5v + 10.5625 + v2 = 1 + 10.5625 Reorder the terms: 10.5625 + -6.5v + v2 = 1 + 10.5625 Combine like terms: 1 + 10.5625 = 11.5625 10.5625 + -6.5v + v2 = 11.5625 Factor a perfect square on the left side: (v + -3.25)(v + -3.25) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (v + -3.25) equal to 3.400367627 and -3.400367627.Subproblem 1
v + -3.25 = 3.400367627 Simplifying v + -3.25 = 3.400367627 Reorder the terms: -3.25 + v = 3.400367627 Solving -3.25 + v = 3.400367627 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + v = 3.400367627 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + v = 3.400367627 + 3.25 v = 3.400367627 + 3.25 Combine like terms: 3.400367627 + 3.25 = 6.650367627 v = 6.650367627 Simplifying v = 6.650367627Subproblem 2
v + -3.25 = -3.400367627 Simplifying v + -3.25 = -3.400367627 Reorder the terms: -3.25 + v = -3.400367627 Solving -3.25 + v = -3.400367627 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + v = -3.400367627 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + v = -3.400367627 + 3.25 v = -3.400367627 + 3.25 Combine like terms: -3.400367627 + 3.25 = -0.150367627 v = -0.150367627 Simplifying v = -0.150367627Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.650367627, -0.150367627}
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