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Simplifying 20j2 + -140je + 245e2 = 0 Reorder the terms: -140ej + 245e2 + 20j2 = 0 Solving -140ej + 245e2 + 20j2 = 0 Solving for variable 'e'. Factor out the Greatest Common Factor (GCF), '5'. 5(-28ej + 49e2 + 4j2) = 0 Factor a trinomial. 5((7e + -2j)(7e + -2j)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7e + -2j)' equal to zero and attempt to solve: Simplifying 7e + -2j = 0 Solving 7e + -2j = 0 Move all terms containing e to the left, all other terms to the right. Add '2j' to each side of the equation. 7e + -2j + 2j = 0 + 2j Combine like terms: -2j + 2j = 0 7e + 0 = 0 + 2j 7e = 0 + 2j Remove the zero: 7e = 2j Divide each side by '7'. e = 0.2857142857j Simplifying e = 0.2857142857jSubproblem 2
Set the factor '(7e + -2j)' equal to zero and attempt to solve: Simplifying 7e + -2j = 0 Solving 7e + -2j = 0 Move all terms containing e to the left, all other terms to the right. Add '2j' to each side of the equation. 7e + -2j + 2j = 0 + 2j Combine like terms: -2j + 2j = 0 7e + 0 = 0 + 2j 7e = 0 + 2j Remove the zero: 7e = 2j Divide each side by '7'. e = 0.2857142857j Simplifying e = 0.2857142857jSolution
e = {0.2857142857j, 0.2857142857j}
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