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Simplifying (-5v2 + 4 + -3) + (4v2 + 6v + 2) = 0 Reorder the terms: (4 + -3 + -5v2) + (4v2 + 6v + 2) = 0 Combine like terms: 4 + -3 = 1 (1 + -5v2) + (4v2 + 6v + 2) = 0 Remove parenthesis around (1 + -5v2) 1 + -5v2 + (4v2 + 6v + 2) = 0 Reorder the terms: 1 + -5v2 + (2 + 6v + 4v2) = 0 Remove parenthesis around (2 + 6v + 4v2) 1 + -5v2 + 2 + 6v + 4v2 = 0 Reorder the terms: 1 + 2 + 6v + -5v2 + 4v2 = 0 Combine like terms: 1 + 2 = 3 3 + 6v + -5v2 + 4v2 = 0 Combine like terms: -5v2 + 4v2 = -1v2 3 + 6v + -1v2 = 0 Solving 3 + 6v + -1v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -6v + v2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -6v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + -6v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6v + v2 = 0 + 3 -6v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6v + v2 = 3 The v term is -6v. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6v + 9 + v2 = 3 + 9 Reorder the terms: 9 + -6v + v2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6v + v2 = 12 Factor a perfect square on the left side: (v + -3)(v + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (v + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
v + -3 = 3.464101615 Simplifying v + -3 = 3.464101615 Reorder the terms: -3 + v = 3.464101615 Solving -3 + v = 3.464101615 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + v = 3.464101615 + 3 v = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 v = 6.464101615 Simplifying v = 6.464101615Subproblem 2
v + -3 = -3.464101615 Simplifying v + -3 = -3.464101615 Reorder the terms: -3 + v = -3.464101615 Solving -3 + v = -3.464101615 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + v = -3.464101615 + 3 v = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 v = -0.464101615 Simplifying v = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.464101615, -0.464101615}
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