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Simplifying v5 + 7v3 + -10v = 0 Reorder the terms: -10v + 7v3 + v5 = 0 Solving -10v + 7v3 + v5 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), 'v'. v(-10 + 7v2 + v4) = 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 '(-10 + 7v2 + v4)' equal to zero and attempt to solve: Simplifying -10 + 7v2 + v4 = 0 Solving -10 + 7v2 + v4 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 7v2 + 10 + v4 = 0 + 10 Reorder the terms: -10 + 10 + 7v2 + v4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 7v2 + v4 = 0 + 10 7v2 + v4 = 0 + 10 Combine like terms: 0 + 10 = 10 7v2 + v4 = 10 The v term is 7v2. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7v2 + 12.25 + v4 = 10 + 12.25 Reorder the terms: 12.25 + 7v2 + v4 = 10 + 12.25 Combine like terms: 10 + 12.25 = 22.25 12.25 + 7v2 + v4 = 22.25 Factor a perfect square on the left side: (v2 + 3.5)(v2 + 3.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (v2 + 3.5) equal to 4.716990566 and -4.716990566.Subproblem 1
v2 + 3.5 = 4.716990566 Simplifying v2 + 3.5 = 4.716990566 Reorder the terms: 3.5 + v2 = 4.716990566 Solving 3.5 + v2 = 4.716990566 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v2 = 4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v2 = 4.716990566 + -3.5 v2 = 4.716990566 + -3.5 Combine like terms: 4.716990566 + -3.5 = 1.216990566 v2 = 1.216990566 Simplifying v2 = 1.216990566 Take the square root of each side: v = {-1.103172954, 1.103172954}Subproblem 2
v2 + 3.5 = -4.716990566 Simplifying v2 + 3.5 = -4.716990566 Reorder the terms: 3.5 + v2 = -4.716990566 Solving 3.5 + v2 = -4.716990566 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v2 = -4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v2 = -4.716990566 + -3.5 v2 = -4.716990566 + -3.5 Combine like terms: -4.716990566 + -3.5 = -8.216990566 v2 = -8.216990566 Simplifying v2 = -8.216990566 Reorder the terms: 8.216990566 + v2 = -8.216990566 + 8.216990566 Combine like terms: -8.216990566 + 8.216990566 = 0.000000000 8.216990566 + v2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
v = {0}
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