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Simplifying 10i2 + -24i + -8 = 0 Reorder the terms: -8 + -24i + 10i2 = 0 Solving -8 + -24i + 10i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -12i + 5i2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -12i + 5i2)' equal to zero and attempt to solve: Simplifying -4 + -12i + 5i2 = 0 Solving -4 + -12i + 5i2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -2.4i + i2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -2.4i + 0.8 + i2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -2.4i + i2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -2.4i + i2 = 0 + 0.8 -2.4i + i2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -2.4i + i2 = 0.8 The i term is -2.4i. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4i + 1.44 + i2 = 0.8 + 1.44 Reorder the terms: 1.44 + -2.4i + i2 = 0.8 + 1.44 Combine like terms: 0.8 + 1.44 = 2.24 1.44 + -2.4i + i2 = 2.24 Factor a perfect square on the left side: (i + -1.2)(i + -1.2) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (i + -1.2) equal to 1.496662955 and -1.496662955.Subproblem 1
i + -1.2 = 1.496662955 Simplifying i + -1.2 = 1.496662955 Reorder the terms: -1.2 + i = 1.496662955 Solving -1.2 + i = 1.496662955 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + i = 1.496662955 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + i = 1.496662955 + 1.2 i = 1.496662955 + 1.2 Combine like terms: 1.496662955 + 1.2 = 2.696662955 i = 2.696662955 Simplifying i = 2.696662955Subproblem 2
i + -1.2 = -1.496662955 Simplifying i + -1.2 = -1.496662955 Reorder the terms: -1.2 + i = -1.496662955 Solving -1.2 + i = -1.496662955 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + i = -1.496662955 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + i = -1.496662955 + 1.2 i = -1.496662955 + 1.2 Combine like terms: -1.496662955 + 1.2 = -0.296662955 i = -0.296662955 Simplifying i = -0.296662955Solution
The solution to the problem is based on the solutions from the subproblems. i = {2.696662955, -0.296662955}Solution
i = {2.696662955, -0.296662955}
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