# algebra

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solve for x

(24+2x)(10+2x) - 240 = 152

First multiply.
24(10) = ___
2x (2x) = ____

Now subtract 240.

Can you finish the problem from here?

dont i need to put this in equatic equation to solve for x. cause i need to find the width of a small rectangle inside a bigger triangle.

Your equation looks o.k. to me. All you have to do is solve for x.

ok this is what i did

foil it. brings 152 over to the left side of the equation

combine like terms

4x^2+20x-104

4(x^2+5-26)

help with magic number? Thanks.

I get 68x for the second term. Recheck.

If you are going to solve the quadratic equation by trial and error anyway, then you don't need to write it in standard form first.

In this case you can write it as:

(24+2x)(10+2x) - 240 = 152 --->

(24+2x)(10+2x) = 392 = 2*14^2

You can easily see a way to get two factors of 14 and one factor of 2: Take x = 2. The other solution can be found as follows. The quadratic function (24+2x)(10+2x) is zero at x = -12 and x = -5 and is therefore symmetrical about the average of these two points, i.e. x = -(8+1/2)

If x = 2 is a solution of the equation (i.e. makes the quadratic function equal to 392), then so must the point:

x = -(8+1/2) - [2 - -(8+1/2)]

= -19

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