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Simplifying 0 = 25i2 + 20i + 25 Reorder the terms: 0 = 25 + 20i + 25i2 Solving 0 = 25 + 20i + 25i2 Solving for variable 'i'. Combine like terms: 0 + -25 = -25 -25 + -20i + -25i2 = 25 + 20i + 25i2 + -25 + -20i + -25i2 Reorder the terms: -25 + -20i + -25i2 = 25 + -25 + 20i + -20i + 25i2 + -25i2 Combine like terms: 25 + -25 = 0 -25 + -20i + -25i2 = 0 + 20i + -20i + 25i2 + -25i2 -25 + -20i + -25i2 = 20i + -20i + 25i2 + -25i2 Combine like terms: 20i + -20i = 0 -25 + -20i + -25i2 = 0 + 25i2 + -25i2 -25 + -20i + -25i2 = 25i2 + -25i2 Combine like terms: 25i2 + -25i2 = 0 -25 + -20i + -25i2 = 0 Factor out the Greatest Common Factor (GCF), '-5'. -5(5 + 4i + 5i2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(5 + 4i + 5i2)' equal to zero and attempt to solve: Simplifying 5 + 4i + 5i2 = 0 Solving 5 + 4i + 5i2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 0.8i + i2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.8i + -1 + i2 = 0 + -1 Reorder the terms: 1 + -1 + 0.8i + i2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.8i + i2 = 0 + -1 0.8i + i2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.8i + i2 = -1 The i term is 0.8i. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8i + 0.16 + i2 = -1 + 0.16 Reorder the terms: 0.16 + 0.8i + i2 = -1 + 0.16 Combine like terms: -1 + 0.16 = -0.84 0.16 + 0.8i + i2 = -0.84 Factor a perfect square on the left side: (i + 0.4)(i + 0.4) = -0.84 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. The solution to this equation could not be determined.
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