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Simplifying 4v2 + -11v + -6 = 0 Reorder the terms: -6 + -11v + 4v2 = 0 Solving -6 + -11v + 4v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -2.75v + v2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.75v + 1.5 + v2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.75v + v2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.75v + v2 = 0 + 1.5 -2.75v + v2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.75v + v2 = 1.5 The v term is -2.75v. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75v + 1.890625 + v2 = 1.5 + 1.890625 Reorder the terms: 1.890625 + -2.75v + v2 = 1.5 + 1.890625 Combine like terms: 1.5 + 1.890625 = 3.390625 1.890625 + -2.75v + v2 = 3.390625 Factor a perfect square on the left side: (v + -1.375)(v + -1.375) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (v + -1.375) equal to 1.841364983 and -1.841364983.Subproblem 1
v + -1.375 = 1.841364983 Simplifying v + -1.375 = 1.841364983 Reorder the terms: -1.375 + v = 1.841364983 Solving -1.375 + v = 1.841364983 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + v = 1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + v = 1.841364983 + 1.375 v = 1.841364983 + 1.375 Combine like terms: 1.841364983 + 1.375 = 3.216364983 v = 3.216364983 Simplifying v = 3.216364983Subproblem 2
v + -1.375 = -1.841364983 Simplifying v + -1.375 = -1.841364983 Reorder the terms: -1.375 + v = -1.841364983 Solving -1.375 + v = -1.841364983 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + v = -1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + v = -1.841364983 + 1.375 v = -1.841364983 + 1.375 Combine like terms: -1.841364983 + 1.375 = -0.466364983 v = -0.466364983 Simplifying v = -0.466364983Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.216364983, -0.466364983}
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