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Simplifying 6i2 + 17i + 23 = 0 Reorder the terms: 23 + 17i + 6i2 = 0 Solving 23 + 17i + 6i2 = 0 Solving for variable 'i'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.833333333 + 2.833333333i + i2 = 0 Move the constant term to the right: Add '-3.833333333' to each side of the equation. 3.833333333 + 2.833333333i + -3.833333333 + i2 = 0 + -3.833333333 Reorder the terms: 3.833333333 + -3.833333333 + 2.833333333i + i2 = 0 + -3.833333333 Combine like terms: 3.833333333 + -3.833333333 = 0.000000000 0.000000000 + 2.833333333i + i2 = 0 + -3.833333333 2.833333333i + i2 = 0 + -3.833333333 Combine like terms: 0 + -3.833333333 = -3.833333333 2.833333333i + i2 = -3.833333333 The i term is 2.833333333i. Take half its coefficient (1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. 2.833333333i + 2.006944445 + i2 = -3.833333333 + 2.006944445 Reorder the terms: 2.006944445 + 2.833333333i + i2 = -3.833333333 + 2.006944445 Combine like terms: -3.833333333 + 2.006944445 = -1.826388888 2.006944445 + 2.833333333i + i2 = -1.826388888 Factor a perfect square on the left side: (i + 1.416666667)(i + 1.416666667) = -1.826388888 Can't calculate square root of the right side. The solution to this equation could not be determined.
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