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Simplifying I(x) = 6000x + -4x2 Multiply I * x xI = 6000x + -4x2 Solving xI = 6000x + -4x2 Solving for variable 'x'. Reorder the terms: -6000x + xI + 4x2 = 6000x + -4x2 + -6000x + 4x2 Reorder the terms: -6000x + xI + 4x2 = 6000x + -6000x + -4x2 + 4x2 Combine like terms: 6000x + -6000x = 0 -6000x + xI + 4x2 = 0 + -4x2 + 4x2 -6000x + xI + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -6000x + xI + 4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-6000 + I + 4x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-6000 + I + 4x)' equal to zero and attempt to solve: Simplifying -6000 + I + 4x = 0 Solving -6000 + I + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '6000' to each side of the equation. -6000 + I + 6000 + 4x = 0 + 6000 Reorder the terms: -6000 + 6000 + I + 4x = 0 + 6000 Combine like terms: -6000 + 6000 = 0 0 + I + 4x = 0 + 6000 I + 4x = 0 + 6000 Combine like terms: 0 + 6000 = 6000 I + 4x = 6000 Add '-1I' to each side of the equation. I + -1I + 4x = 6000 + -1I Combine like terms: I + -1I = 0 0 + 4x = 6000 + -1I 4x = 6000 + -1I Divide each side by '4'. x = 1500 + -0.25I Simplifying x = 1500 + -0.25ISolution
x = {0, 1500 + -0.25I}
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