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Simplifying 4v(2v2 + -6v + -6) = 0 Reorder the terms: 4v(-6 + -6v + 2v2) = 0 (-6 * 4v + -6v * 4v + 2v2 * 4v) = 0 (-24v + -24v2 + 8v3) = 0 Solving -24v + -24v2 + 8v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '8v'. 8v(-3 + -3v + v2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(-3 + -3v + v2)' equal to zero and attempt to solve: Simplifying -3 + -3v + v2 = 0 Solving -3 + -3v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -3v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + -3v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3v + v2 = 0 + 3 -3v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3v + v2 = 3 The v term is -3v. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3v + 2.25 + v2 = 3 + 2.25 Reorder the terms: 2.25 + -3v + v2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + -3v + v2 = 5.25 Factor a perfect square on the left side: (v + -1.5)(v + -1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (v + -1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
v + -1.5 = 2.291287847 Simplifying v + -1.5 = 2.291287847 Reorder the terms: -1.5 + v = 2.291287847 Solving -1.5 + v = 2.291287847 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + v = 2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = 2.291287847 + 1.5 v = 2.291287847 + 1.5 Combine like terms: 2.291287847 + 1.5 = 3.791287847 v = 3.791287847 Simplifying v = 3.791287847Subproblem 2
v + -1.5 = -2.291287847 Simplifying v + -1.5 = -2.291287847 Reorder the terms: -1.5 + v = -2.291287847 Solving -1.5 + v = -2.291287847 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + v = -2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = -2.291287847 + 1.5 v = -2.291287847 + 1.5 Combine like terms: -2.291287847 + 1.5 = -0.791287847 v = -0.791287847 Simplifying v = -0.791287847Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.791287847, -0.791287847}Solution
v = {0, 3.791287847, -0.791287847}
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