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Simplifying (-4v2 + 7v + -3) + (2v2 + 5v + 6) = 0 Reorder the terms: (-3 + 7v + -4v2) + (2v2 + 5v + 6) = 0 Remove parenthesis around (-3 + 7v + -4v2) -3 + 7v + -4v2 + (2v2 + 5v + 6) = 0 Reorder the terms: -3 + 7v + -4v2 + (6 + 5v + 2v2) = 0 Remove parenthesis around (6 + 5v + 2v2) -3 + 7v + -4v2 + 6 + 5v + 2v2 = 0 Reorder the terms: -3 + 6 + 7v + 5v + -4v2 + 2v2 = 0 Combine like terms: -3 + 6 = 3 3 + 7v + 5v + -4v2 + 2v2 = 0 Combine like terms: 7v + 5v = 12v 3 + 12v + -4v2 + 2v2 = 0 Combine like terms: -4v2 + 2v2 = -2v2 3 + 12v + -2v2 = 0 Solving 3 + 12v + -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'. -1.5 + -6v + v2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -6v + 1.5 + v2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -6v + v2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -6v + v2 = 0 + 1.5 -6v + v2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -6v + v2 = 1.5 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 = 1.5 + 9 Reorder the terms: 9 + -6v + v2 = 1.5 + 9 Combine like terms: 1.5 + 9 = 10.5 9 + -6v + v2 = 10.5 Factor a perfect square on the left side: (v + -3)(v + -3) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (v + -3) equal to 3.240370349 and -3.240370349.Subproblem 1
v + -3 = 3.240370349 Simplifying v + -3 = 3.240370349 Reorder the terms: -3 + v = 3.240370349 Solving -3 + v = 3.240370349 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 = 3.240370349 + 3 Combine like terms: -3 + 3 = 0 0 + v = 3.240370349 + 3 v = 3.240370349 + 3 Combine like terms: 3.240370349 + 3 = 6.240370349 v = 6.240370349 Simplifying v = 6.240370349Subproblem 2
v + -3 = -3.240370349 Simplifying v + -3 = -3.240370349 Reorder the terms: -3 + v = -3.240370349 Solving -3 + v = -3.240370349 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 = -3.240370349 + 3 Combine like terms: -3 + 3 = 0 0 + v = -3.240370349 + 3 v = -3.240370349 + 3 Combine like terms: -3.240370349 + 3 = -0.240370349 v = -0.240370349 Simplifying v = -0.240370349Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.240370349, -0.240370349}
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