Recall that variables represent changing values. In this unit, you will work with equations that contain two different variables. What types of situations might be
modeled with equations containing two or more variables? If the value of one
variable changes, must the value of the other variable change for the equation
to remain true? How would the number of solutions for an equation with two
variables differ from the number of solutions for an equation with only one?
Explain.

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6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4