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Simplifying 9i2 + 40i + -16 = 0factored Reorder the terms: -16 + 40i + 9i2 = 0factored Anything times zero is zero. -16 + 40i + 9i2 = 0acdefort Solving -16 + 40i + 9i2 = 0 Solving for variable 'i'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + 4.444444444i + i2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + 4.444444444i + 1.777777778 + i2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + 4.444444444i + i2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + 4.444444444i + i2 = 0 + 1.777777778 4.444444444i + i2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 4.444444444i + i2 = 1.777777778 The i term is 4.444444444i. Take half its coefficient (2.222222222). Square it (4.938271604) and add it to both sides. Add '4.938271604' to each side of the equation. 4.444444444i + 4.938271604 + i2 = 1.777777778 + 4.938271604 Reorder the terms: 4.938271604 + 4.444444444i + i2 = 1.777777778 + 4.938271604 Combine like terms: 1.777777778 + 4.938271604 = 6.716049382 4.938271604 + 4.444444444i + i2 = 6.716049382 Factor a perfect square on the left side: (i + 2.222222222)(i + 2.222222222) = 6.716049382 Calculate the square root of the right side: 2.591534175 Break this problem into two subproblems by setting (i + 2.222222222) equal to 2.591534175 and -2.591534175.Subproblem 1
i + 2.222222222 = 2.591534175 Simplifying i + 2.222222222 = 2.591534175 Reorder the terms: 2.222222222 + i = 2.591534175 Solving 2.222222222 + i = 2.591534175 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2.222222222' to each side of the equation. 2.222222222 + -2.222222222 + i = 2.591534175 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + i = 2.591534175 + -2.222222222 i = 2.591534175 + -2.222222222 Combine like terms: 2.591534175 + -2.222222222 = 0.369311953 i = 0.369311953 Simplifying i = 0.369311953Subproblem 2
i + 2.222222222 = -2.591534175 Simplifying i + 2.222222222 = -2.591534175 Reorder the terms: 2.222222222 + i = -2.591534175 Solving 2.222222222 + i = -2.591534175 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2.222222222' to each side of the equation. 2.222222222 + -2.222222222 + i = -2.591534175 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + i = -2.591534175 + -2.222222222 i = -2.591534175 + -2.222222222 Combine like terms: -2.591534175 + -2.222222222 = -4.813756397 i = -4.813756397 Simplifying i = -4.813756397Solution
The solution to the problem is based on the solutions from the subproblems. i = {0.369311953, -4.813756397}
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