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Simplifying 4 + -1v(v + -6) = -8 Reorder the terms: 4 + -1v(-6 + v) = -8 4 + (-6 * -1v + v * -1v) = -8 4 + (6v + -1v2) = -8 Solving 4 + 6v + -1v2 = -8 Solving for variable 'v'. Reorder the terms: 4 + 8 + 6v + -1v2 = -8 + 8 Combine like terms: 4 + 8 = 12 12 + 6v + -1v2 = -8 + 8 Combine like terms: -8 + 8 = 0 12 + 6v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -6v + v2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -6v + 12 + v2 = 0 + 12 Reorder the terms: -12 + 12 + -6v + v2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -6v + v2 = 0 + 12 -6v + v2 = 0 + 12 Combine like terms: 0 + 12 = 12 -6v + v2 = 12 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 = 12 + 9 Reorder the terms: 9 + -6v + v2 = 12 + 9 Combine like terms: 12 + 9 = 21 9 + -6v + v2 = 21 Factor a perfect square on the left side: (v + -3)(v + -3) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (v + -3) equal to 4.582575695 and -4.582575695.Subproblem 1
v + -3 = 4.582575695 Simplifying v + -3 = 4.582575695 Reorder the terms: -3 + v = 4.582575695 Solving -3 + v = 4.582575695 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 = 4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + v = 4.582575695 + 3 v = 4.582575695 + 3 Combine like terms: 4.582575695 + 3 = 7.582575695 v = 7.582575695 Simplifying v = 7.582575695Subproblem 2
v + -3 = -4.582575695 Simplifying v + -3 = -4.582575695 Reorder the terms: -3 + v = -4.582575695 Solving -3 + v = -4.582575695 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 = -4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + v = -4.582575695 + 3 v = -4.582575695 + 3 Combine like terms: -4.582575695 + 3 = -1.582575695 v = -1.582575695 Simplifying v = -1.582575695Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.582575695, -1.582575695}
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