# Answer to Question #13621 in Abstract Algebra for Florence

Question #13621

Find the measure, in terms of x, of each side of a square if the Area = x^2– 16x +64.

Factor and solve.

x^2-x-72=0

2x^2+9x-5=0

x^2-64=0

4x^2-36x+72

Factor and solve.

x^2-x-72=0

2x^2+9x-5=0

x^2-64=0

4x^2-36x+72

Expert's answer

Area = x^2– 16x +64=(x-8)^2 => the side=x-8

x^2-x-72=(x-9)(x+8)

D=1+72*4=289

x1,1=(1+-17)/2

x1=9, x2=-8

2x^2+9x-5=0

D=81+40=121

x1,2=(-9+-11)/4

x1=-5, x2=1/2

x^2-64=(x-8)(x+8)=0

therefore x1=8, x2=-8

4x^2-36x+72=0

x^2-9x+18=(x-6)(x-3)=0

therefore x1=6, x2=3

x^2-x-72=(x-9)(x+8)

D=1+72*4=289

x1,1=(1+-17)/2

x1=9, x2=-8

2x^2+9x-5=0

D=81+40=121

x1,2=(-9+-11)/4

x1=-5, x2=1/2

x^2-64=(x-8)(x+8)=0

therefore x1=8, x2=-8

4x^2-36x+72=0

x^2-9x+18=(x-6)(x-3)=0

therefore x1=6, x2=3

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