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Simplifying I(x) = 420x + -0.1x2 Multiply I * x xI = 420x + -0.1x2 Solving xI = 420x + -0.1x2 Solving for variable 'x'. Reorder the terms: -420x + xI + 0.1x2 = 420x + -0.1x2 + -420x + 0.1x2 Reorder the terms: -420x + xI + 0.1x2 = 420x + -420x + -0.1x2 + 0.1x2 Combine like terms: 420x + -420x = 0 -420x + xI + 0.1x2 = 0 + -0.1x2 + 0.1x2 -420x + xI + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 -420x + xI + 0.1x2 = 0.0 Factor out the Greatest Common Factor (GCF), 'x'. x(-420 + I + 0.1x) = 0.0Subproblem 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 '(-420 + I + 0.1x)' equal to zero and attempt to solve: Simplifying -420 + I + 0.1x = 0 Solving -420 + I + 0.1x = 0 Move all terms containing x to the left, all other terms to the right. Add '420' to each side of the equation. -420 + I + 420 + 0.1x = 0 + 420 Reorder the terms: -420 + 420 + I + 0.1x = 0 + 420 Combine like terms: -420 + 420 = 0 0 + I + 0.1x = 0 + 420 I + 0.1x = 0 + 420 Combine like terms: 0 + 420 = 420 I + 0.1x = 420 Add '-1I' to each side of the equation. I + -1I + 0.1x = 420 + -1I Combine like terms: I + -1I = 0 0 + 0.1x = 420 + -1I 0.1x = 420 + -1I Divide each side by '0.1'. x = 4200 + -10I Simplifying x = 4200 + -10ISolution
x = {0, 4200 + -10I}
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