(16•16)+(12•12)=(x+12)(x+12)

Question

Find x. Assume that segments that appear to be tangent are tangent.

Answer 1

You have no figure associated with the given equation.

 

Taking square roots of each side of your equation, you get x+12 = √(400)

so x+12 = 20 so x = 8 (I'm ignoring the extraneous answer based on -20 on right side since this is Geometry).

Answer 2

Do you just want all solutions to the equation ?

(16*16)+(12*12)=(x+12)(x+12)

256+(144)=x^2+24x+144

subtract 144 from both sides

256=x^2+24x

x^2+24x-256=0

factor

256=2*2*2*2*2*2*2*2=(2*2*2)*(2*2*2*2*2)=8*32 and 32-8=24

(x+32)(x-8)=0

x-8=0

x=8,or...

x+32=0

x=-32

another solution...

(16)(16)+(12)(12)=256+144=400

400=20*20 or 400=(-20)(-20)

(x+12)(x+12)=20*20

x+12=20

x=8

x+12=-20

x=-32