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Simplifying -4e2 + 7e3 + -9e4 = 0 Solving -4e2 + 7e3 + -9e4 = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), 'e2'. e2(-4 + 7e + -9e2) = 0Subproblem 1
Set the factor 'e2' equal to zero and attempt to solve: Simplifying e2 = 0 Solving e2 = 0 Move all terms containing e to the left, all other terms to the right. Simplifying e2 = 0 Take the square root of each side: e = {0}Subproblem 2
Set the factor '(-4 + 7e + -9e2)' equal to zero and attempt to solve: Simplifying -4 + 7e + -9e2 = 0 Solving -4 + 7e + -9e2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.4444444444 + -0.7777777778e + e2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -0.7777777778e + -0.4444444444 + e2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -0.7777777778e + e2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -0.7777777778e + e2 = 0 + -0.4444444444 -0.7777777778e + e2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -0.7777777778e + e2 = -0.4444444444 The e term is -0.7777777778e. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778e + 0.1512345679 + e2 = -0.4444444444 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778e + e2 = -0.4444444444 + 0.1512345679 Combine like terms: -0.4444444444 + 0.1512345679 = -0.2932098765 0.1512345679 + -0.7777777778e + e2 = -0.2932098765 Factor a perfect square on the left side: (e + -0.3888888889)(e + -0.3888888889) = -0.2932098765 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
e = {0}
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