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Simplifying -196v3 + 28v2 + v = 0 Reorder the terms: v + 28v2 + -196v3 = 0 Solving v + 28v2 + -196v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), 'v'. v(1 + 28v + -196v2) = 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 '(1 + 28v + -196v2)' equal to zero and attempt to solve: Simplifying 1 + 28v + -196v2 = 0 Solving 1 + 28v + -196v2 = 0 Begin completing the square. Divide all terms by -196 the coefficient of the squared term: Divide each side by '-196'. -0.005102040816 + -0.1428571429v + v2 = 0 Move the constant term to the right: Add '0.005102040816' to each side of the equation. -0.005102040816 + -0.1428571429v + 0.005102040816 + v2 = 0 + 0.005102040816 Reorder the terms: -0.005102040816 + 0.005102040816 + -0.1428571429v + v2 = 0 + 0.005102040816 Combine like terms: -0.005102040816 + 0.005102040816 = 0.000000000000 0.000000000000 + -0.1428571429v + v2 = 0 + 0.005102040816 -0.1428571429v + v2 = 0 + 0.005102040816 Combine like terms: 0 + 0.005102040816 = 0.005102040816 -0.1428571429v + v2 = 0.005102040816 The v term is -0.1428571429v. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429v + 0.005102040819 + v2 = 0.005102040816 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429v + v2 = 0.005102040816 + 0.005102040819 Combine like terms: 0.005102040816 + 0.005102040819 = 0.010204081635 0.005102040819 + -0.1428571429v + v2 = 0.010204081635 Factor a perfect square on the left side: (v + -0.07142857145)(v + -0.07142857145) = 0.010204081635 Calculate the square root of the right side: 0.101015254 Break this problem into two subproblems by setting (v + -0.07142857145) equal to 0.101015254 and -0.101015254.Subproblem 1
v + -0.07142857145 = 0.101015254 Simplifying v + -0.07142857145 = 0.101015254 Reorder the terms: -0.07142857145 + v = 0.101015254 Solving -0.07142857145 + v = 0.101015254 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + v = 0.101015254 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + v = 0.101015254 + 0.07142857145 v = 0.101015254 + 0.07142857145 Combine like terms: 0.101015254 + 0.07142857145 = 0.17244382545 v = 0.17244382545 Simplifying v = 0.17244382545Subproblem 2
v + -0.07142857145 = -0.101015254 Simplifying v + -0.07142857145 = -0.101015254 Reorder the terms: -0.07142857145 + v = -0.101015254 Solving -0.07142857145 + v = -0.101015254 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + v = -0.101015254 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + v = -0.101015254 + 0.07142857145 v = -0.101015254 + 0.07142857145 Combine like terms: -0.101015254 + 0.07142857145 = -0.02958668255 v = -0.02958668255 Simplifying v = -0.02958668255Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.17244382545, -0.02958668255}Solution
v = {0, 0.17244382545, -0.02958668255}
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