# Algebraic Polynomials

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I don't know where to go about creating a polynomial equations for the following problem: A piece of wire 52 in. long is cut into two pieces, and then each piece is formed into a square. If the sum of the areas of the two squares is 97 in.^2, how long are the pieces of wire? My attempted starting point is 97 = (1/4(x))^2 + ((1/4)(52-x))^2, but my numbers don't seem to work. Help is appreciated!

• Algebraic Polynomials -

What did you get for solution?

• Algebraic Polynomials -

Once I move numbers around to achieve a trinomial, I have (1/8)x^2 - (13/2)x + 72, I'm just not sure how I would factor that.

• Algebraic Polynomials -

Expand
97 = (x/4)^2 + ((52-x)/4)^2
to get
x^2/8-13x/2+72=0
multiply by 8 throughout to get
x^2-52x+576=0
factor and solve for x.
You should get two positive integers which add up to 52.

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