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Simplifying -56i2 + -25i + 56 = 0 Reorder the terms: 56 + -25i + -56i2 = 0 Solving 56 + -25i + -56i2 = 0 Solving for variable 'i'. Begin completing the square. Divide all terms by -56 the coefficient of the squared term: Divide each side by '-56'. -1 + 0.4464285714i + i2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.4464285714i + 1 + i2 = 0 + 1 Reorder the terms: -1 + 1 + 0.4464285714i + i2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.4464285714i + i2 = 0 + 1 0.4464285714i + i2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.4464285714i + i2 = 1 The i term is 0.4464285714i. Take half its coefficient (0.2232142857). Square it (0.04982461734) and add it to both sides. Add '0.04982461734' to each side of the equation. 0.4464285714i + 0.04982461734 + i2 = 1 + 0.04982461734 Reorder the terms: 0.04982461734 + 0.4464285714i + i2 = 1 + 0.04982461734 Combine like terms: 1 + 0.04982461734 = 1.04982461734 0.04982461734 + 0.4464285714i + i2 = 1.04982461734 Factor a perfect square on the left side: (i + 0.2232142857)(i + 0.2232142857) = 1.04982461734 Calculate the square root of the right side: 1.024609495 Break this problem into two subproblems by setting (i + 0.2232142857) equal to 1.024609495 and -1.024609495.Subproblem 1
i + 0.2232142857 = 1.024609495 Simplifying i + 0.2232142857 = 1.024609495 Reorder the terms: 0.2232142857 + i = 1.024609495 Solving 0.2232142857 + i = 1.024609495 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-0.2232142857' to each side of the equation. 0.2232142857 + -0.2232142857 + i = 1.024609495 + -0.2232142857 Combine like terms: 0.2232142857 + -0.2232142857 = 0.0000000000 0.0000000000 + i = 1.024609495 + -0.2232142857 i = 1.024609495 + -0.2232142857 Combine like terms: 1.024609495 + -0.2232142857 = 0.8013952093 i = 0.8013952093 Simplifying i = 0.8013952093Subproblem 2
i + 0.2232142857 = -1.024609495 Simplifying i + 0.2232142857 = -1.024609495 Reorder the terms: 0.2232142857 + i = -1.024609495 Solving 0.2232142857 + i = -1.024609495 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-0.2232142857' to each side of the equation. 0.2232142857 + -0.2232142857 + i = -1.024609495 + -0.2232142857 Combine like terms: 0.2232142857 + -0.2232142857 = 0.0000000000 0.0000000000 + i = -1.024609495 + -0.2232142857 i = -1.024609495 + -0.2232142857 Combine like terms: -1.024609495 + -0.2232142857 = -1.2478237807 i = -1.2478237807 Simplifying i = -1.2478237807Solution
The solution to the problem is based on the solutions from the subproblems. i = {0.8013952093, -1.2478237807}
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