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Simplifying 5v3 + -8v2 + -64v = 0 Reorder the terms: -64v + -8v2 + 5v3 = 0 Solving -64v + -8v2 + 5v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), 'v'. v(-64 + -8v + 5v2) = 0Subproblem 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 '(-64 + -8v + 5v2)' equal to zero and attempt to solve: Simplifying -64 + -8v + 5v2 = 0 Solving -64 + -8v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.8 + -1.6v + v2 = 0 Move the constant term to the right: Add '12.8' to each side of the equation. -12.8 + -1.6v + 12.8 + v2 = 0 + 12.8 Reorder the terms: -12.8 + 12.8 + -1.6v + v2 = 0 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + -1.6v + v2 = 0 + 12.8 -1.6v + v2 = 0 + 12.8 Combine like terms: 0 + 12.8 = 12.8 -1.6v + v2 = 12.8 The v term is -1.6v. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6v + 0.64 + v2 = 12.8 + 0.64 Reorder the terms: 0.64 + -1.6v + v2 = 12.8 + 0.64 Combine like terms: 12.8 + 0.64 = 13.44 0.64 + -1.6v + v2 = 13.44 Factor a perfect square on the left side: (v + -0.8)(v + -0.8) = 13.44 Calculate the square root of the right side: 3.666060556 Break this problem into two subproblems by setting (v + -0.8) equal to 3.666060556 and -3.666060556.Subproblem 1
v + -0.8 = 3.666060556 Simplifying v + -0.8 = 3.666060556 Reorder the terms: -0.8 + v = 3.666060556 Solving -0.8 + v = 3.666060556 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + v = 3.666060556 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + v = 3.666060556 + 0.8 v = 3.666060556 + 0.8 Combine like terms: 3.666060556 + 0.8 = 4.466060556 v = 4.466060556 Simplifying v = 4.466060556Subproblem 2
v + -0.8 = -3.666060556 Simplifying v + -0.8 = -3.666060556 Reorder the terms: -0.8 + v = -3.666060556 Solving -0.8 + v = -3.666060556 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + v = -3.666060556 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + v = -3.666060556 + 0.8 v = -3.666060556 + 0.8 Combine like terms: -3.666060556 + 0.8 = -2.866060556 v = -2.866060556 Simplifying v = -2.866060556Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.466060556, -2.866060556}Solution
v = {0, 4.466060556, -2.866060556}
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