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Simplifying (-6v2 + 3v + -4) + (5v2 + 7v + 1) = 0 Reorder the terms: (-4 + 3v + -6v2) + (5v2 + 7v + 1) = 0 Remove parenthesis around (-4 + 3v + -6v2) -4 + 3v + -6v2 + (5v2 + 7v + 1) = 0 Reorder the terms: -4 + 3v + -6v2 + (1 + 7v + 5v2) = 0 Remove parenthesis around (1 + 7v + 5v2) -4 + 3v + -6v2 + 1 + 7v + 5v2 = 0 Reorder the terms: -4 + 1 + 3v + 7v + -6v2 + 5v2 = 0 Combine like terms: -4 + 1 = -3 -3 + 3v + 7v + -6v2 + 5v2 = 0 Combine like terms: 3v + 7v = 10v -3 + 10v + -6v2 + 5v2 = 0 Combine like terms: -6v2 + 5v2 = -1v2 -3 + 10v + -1v2 = 0 Solving -3 + 10v + -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 + -10v + v2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -10v + -3 + v2 = 0 + -3 Reorder the terms: 3 + -3 + -10v + v2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10v + v2 = 0 + -3 -10v + v2 = 0 + -3 Combine like terms: 0 + -3 = -3 -10v + v2 = -3 The v term is -10v. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10v + 25 + v2 = -3 + 25 Reorder the terms: 25 + -10v + v2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + -10v + v2 = 22 Factor a perfect square on the left side: (v + -5)(v + -5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (v + -5) equal to 4.69041576 and -4.69041576.Subproblem 1
v + -5 = 4.69041576 Simplifying v + -5 = 4.69041576 Reorder the terms: -5 + v = 4.69041576 Solving -5 + v = 4.69041576 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = 4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + v = 4.69041576 + 5 v = 4.69041576 + 5 Combine like terms: 4.69041576 + 5 = 9.69041576 v = 9.69041576 Simplifying v = 9.69041576Subproblem 2
v + -5 = -4.69041576 Simplifying v + -5 = -4.69041576 Reorder the terms: -5 + v = -4.69041576 Solving -5 + v = -4.69041576 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = -4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + v = -4.69041576 + 5 v = -4.69041576 + 5 Combine like terms: -4.69041576 + 5 = 0.30958424 v = 0.30958424 Simplifying v = 0.30958424Solution
The solution to the problem is based on the solutions from the subproblems. v = {9.69041576, 0.30958424}
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