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Simplifying (2v2 + -3v + 4) + -1(-6v2 + v + 5) = 0 Reorder the terms: (4 + -3v + 2v2) + -1(-6v2 + v + 5) = 0 Remove parenthesis around (4 + -3v + 2v2) 4 + -3v + 2v2 + -1(-6v2 + v + 5) = 0 Reorder the terms: 4 + -3v + 2v2 + -1(5 + v + -6v2) = 0 4 + -3v + 2v2 + (5 * -1 + v * -1 + -6v2 * -1) = 0 4 + -3v + 2v2 + (-5 + -1v + 6v2) = 0 Reorder the terms: 4 + -5 + -3v + -1v + 2v2 + 6v2 = 0 Combine like terms: 4 + -5 = -1 -1 + -3v + -1v + 2v2 + 6v2 = 0 Combine like terms: -3v + -1v = -4v -1 + -4v + 2v2 + 6v2 = 0 Combine like terms: 2v2 + 6v2 = 8v2 -1 + -4v + 8v2 = 0 Solving -1 + -4v + 8v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.5v + v2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.5v + 0.125 + v2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.5v + v2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.5v + v2 = 0 + 0.125 -0.5v + v2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.5v + v2 = 0.125 The v term is -0.5v. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5v + 0.0625 + v2 = 0.125 + 0.0625 Reorder the terms: 0.0625 + -0.5v + v2 = 0.125 + 0.0625 Combine like terms: 0.125 + 0.0625 = 0.1875 0.0625 + -0.5v + v2 = 0.1875 Factor a perfect square on the left side: (v + -0.25)(v + -0.25) = 0.1875 Calculate the square root of the right side: 0.433012702 Break this problem into two subproblems by setting (v + -0.25) equal to 0.433012702 and -0.433012702.Subproblem 1
v + -0.25 = 0.433012702 Simplifying v + -0.25 = 0.433012702 Reorder the terms: -0.25 + v = 0.433012702 Solving -0.25 + v = 0.433012702 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + v = 0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + v = 0.433012702 + 0.25 v = 0.433012702 + 0.25 Combine like terms: 0.433012702 + 0.25 = 0.683012702 v = 0.683012702 Simplifying v = 0.683012702Subproblem 2
v + -0.25 = -0.433012702 Simplifying v + -0.25 = -0.433012702 Reorder the terms: -0.25 + v = -0.433012702 Solving -0.25 + v = -0.433012702 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + v = -0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + v = -0.433012702 + 0.25 v = -0.433012702 + 0.25 Combine like terms: -0.433012702 + 0.25 = -0.183012702 v = -0.183012702 Simplifying v = -0.183012702Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.683012702, -0.183012702}
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