Question 500772
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The area of a triangle is the base times the altitude divided by 2.

Your expression for the base is spot on, but you didn't multiply by the altitude nor did you divide by 2.

But then you somehow came up with the correct quadratic equation somewhere out of thin air.

Let's follow the steps to get there first:

Base: *[tex \Large 2a\ +\ 14]
Altitude: *[tex \Large a]
Area: *[tex \Large 18]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(2a\ +\ 14)a}{2}\ =\ 18]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2a^2\ +\ 14a\ =\ 36]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2a^2\ +\ 14a\ -\ 36\ =\ 0]

Divide by 2:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^2\ +\ 7a\ -\ 18\ =\ 0]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2\ \times\ 9\ =\ -18]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2\ +\ 9\ =\ 7]

You should be able to get it from there.  Remember to toss out the negative root.

John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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