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Simplifying 28v3 + -40v2 + 400v = 0 Reorder the terms: 400v + -40v2 + 28v3 = 0 Solving 400v + -40v2 + 28v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4v'. 4v(100 + -10v + 7v2) = 0 Ignore the factor 4.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 '(100 + -10v + 7v2)' equal to zero and attempt to solve: Simplifying 100 + -10v + 7v2 = 0 Solving 100 + -10v + 7v2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 14.28571429 + -1.428571429v + v2 = 0 Move the constant term to the right: Add '-14.28571429' to each side of the equation. 14.28571429 + -1.428571429v + -14.28571429 + v2 = 0 + -14.28571429 Reorder the terms: 14.28571429 + -14.28571429 + -1.428571429v + v2 = 0 + -14.28571429 Combine like terms: 14.28571429 + -14.28571429 = 0.00000000 0.00000000 + -1.428571429v + v2 = 0 + -14.28571429 -1.428571429v + v2 = 0 + -14.28571429 Combine like terms: 0 + -14.28571429 = -14.28571429 -1.428571429v + v2 = -14.28571429 The v term is -1.428571429v. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429v + 0.5102040819 + v2 = -14.28571429 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429v + v2 = -14.28571429 + 0.5102040819 Combine like terms: -14.28571429 + 0.5102040819 = -13.7755102081 0.5102040819 + -1.428571429v + v2 = -13.7755102081 Factor a perfect square on the left side: (v + -0.7142857145)(v + -0.7142857145) = -13.7755102081 Can't calculate square root of the right side. 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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