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Simplifying 6v2 + -10 = 3v Reorder the terms: -10 + 6v2 = 3v Solving -10 + 6v2 = 3v Solving for variable 'v'. Reorder the terms: -10 + -3v + 6v2 = 3v + -3v Combine like terms: 3v + -3v = 0 -10 + -3v + 6v2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.666666667 + -0.5v + v2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -0.5v + 1.666666667 + v2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -0.5v + v2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -0.5v + v2 = 0 + 1.666666667 -0.5v + v2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -0.5v + v2 = 1.666666667 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 = 1.666666667 + 0.0625 Reorder the terms: 0.0625 + -0.5v + v2 = 1.666666667 + 0.0625 Combine like terms: 1.666666667 + 0.0625 = 1.729166667 0.0625 + -0.5v + v2 = 1.729166667 Factor a perfect square on the left side: (v + -0.25)(v + -0.25) = 1.729166667 Calculate the square root of the right side: 1.31497782 Break this problem into two subproblems by setting (v + -0.25) equal to 1.31497782 and -1.31497782.Subproblem 1
v + -0.25 = 1.31497782 Simplifying v + -0.25 = 1.31497782 Reorder the terms: -0.25 + v = 1.31497782 Solving -0.25 + v = 1.31497782 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 = 1.31497782 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + v = 1.31497782 + 0.25 v = 1.31497782 + 0.25 Combine like terms: 1.31497782 + 0.25 = 1.56497782 v = 1.56497782 Simplifying v = 1.56497782Subproblem 2
v + -0.25 = -1.31497782 Simplifying v + -0.25 = -1.31497782 Reorder the terms: -0.25 + v = -1.31497782 Solving -0.25 + v = -1.31497782 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 = -1.31497782 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + v = -1.31497782 + 0.25 v = -1.31497782 + 0.25 Combine like terms: -1.31497782 + 0.25 = -1.06497782 v = -1.06497782 Simplifying v = -1.06497782Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.56497782, -1.06497782}
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