Ex: Find the x-intercept of a Tangent Line

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This video explains how to determine the equation of a tangent line and find the x-intercept of the tangent line.
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I like this and all but the sidetracking with fractions is slowing my understanding. I get the idea is to not have to evaluate 0.8^3 and whatnot, but I'd rather just accept the output is 0.512 and move on with what's relevant.
Otherwise, great and thanks.

JamesWalker-dumr