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Simplifying 2v2 + -7v + -6 = (v + -2) Reorder the terms: -6 + -7v + 2v2 = (v + -2) Reorder the terms: -6 + -7v + 2v2 = (-2 + v) Remove parenthesis around (-2 + v) -6 + -7v + 2v2 = -2 + v Solving -6 + -7v + 2v2 = -2 + v Solving for variable 'v'. Reorder the terms: -6 + 2 + -7v + -1v + 2v2 = -2 + v + 2 + -1v Combine like terms: -6 + 2 = -4 -4 + -7v + -1v + 2v2 = -2 + v + 2 + -1v Combine like terms: -7v + -1v = -8v -4 + -8v + 2v2 = -2 + v + 2 + -1v Reorder the terms: -4 + -8v + 2v2 = -2 + 2 + v + -1v Combine like terms: -2 + 2 = 0 -4 + -8v + 2v2 = 0 + v + -1v -4 + -8v + 2v2 = v + -1v Combine like terms: v + -1v = 0 -4 + -8v + 2v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -4v + v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -4v + v2)' equal to zero and attempt to solve: Simplifying -2 + -4v + v2 = 0 Solving -2 + -4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -4v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + -4v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4v + v2 = 0 + 2 -4v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4v + v2 = 2 The v term is -4v. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4v + 4 + v2 = 2 + 4 Reorder the terms: 4 + -4v + v2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4v + v2 = 6 Factor a perfect square on the left side: (v + -2)(v + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (v + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
v + -2 = 2.449489743 Simplifying v + -2 = 2.449489743 Reorder the terms: -2 + v = 2.449489743 Solving -2 + v = 2.449489743 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + v = 2.449489743 + 2 v = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 v = 4.449489743 Simplifying v = 4.449489743Subproblem 2
v + -2 = -2.449489743 Simplifying v + -2 = -2.449489743 Reorder the terms: -2 + v = -2.449489743 Solving -2 + v = -2.449489743 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + v = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + v = -2.449489743 + 2 v = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 v = -0.449489743 Simplifying v = -0.449489743Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.449489743, -0.449489743}Solution
v = {4.449489743, -0.449489743}
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