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Simplifying -1v(v + 7) + -3(1 + -6v) = 0 Reorder the terms: -1v(7 + v) + -3(1 + -6v) = 0 (7 * -1v + v * -1v) + -3(1 + -6v) = 0 (-7v + -1v2) + -3(1 + -6v) = 0 -7v + -1v2 + (1 * -3 + -6v * -3) = 0 -7v + -1v2 + (-3 + 18v) = 0 Reorder the terms: -3 + -7v + 18v + -1v2 = 0 Combine like terms: -7v + 18v = 11v -3 + 11v + -1v2 = 0 Solving -3 + 11v + -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 + -11v + v2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -11v + -3 + v2 = 0 + -3 Reorder the terms: 3 + -3 + -11v + v2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11v + v2 = 0 + -3 -11v + v2 = 0 + -3 Combine like terms: 0 + -3 = -3 -11v + v2 = -3 The v term is -11v. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11v + 30.25 + v2 = -3 + 30.25 Reorder the terms: 30.25 + -11v + v2 = -3 + 30.25 Combine like terms: -3 + 30.25 = 27.25 30.25 + -11v + v2 = 27.25 Factor a perfect square on the left side: (v + -5.5)(v + -5.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (v + -5.5) equal to 5.220153254 and -5.220153254.Subproblem 1
v + -5.5 = 5.220153254 Simplifying v + -5.5 = 5.220153254 Reorder the terms: -5.5 + v = 5.220153254 Solving -5.5 + v = 5.220153254 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = 5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = 5.220153254 + 5.5 v = 5.220153254 + 5.5 Combine like terms: 5.220153254 + 5.5 = 10.720153254 v = 10.720153254 Simplifying v = 10.720153254Subproblem 2
v + -5.5 = -5.220153254 Simplifying v + -5.5 = -5.220153254 Reorder the terms: -5.5 + v = -5.220153254 Solving -5.5 + v = -5.220153254 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = -5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = -5.220153254 + 5.5 v = -5.220153254 + 5.5 Combine like terms: -5.220153254 + 5.5 = 0.279846746 v = 0.279846746 Simplifying v = 0.279846746Solution
The solution to the problem is based on the solutions from the subproblems. v = {10.720153254, 0.279846746}
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