Eight more than the square of a number is six times the number.  Find the
number.

>>...Eight more than the square of a number is six times the number...<<

Replace the word "eight" by 8 and "six" by 6

>>...8 more than the square of a number is 6 times the number...<<

Let the number = x.  "a number" and "the number" are both talking about
the same number. So replace both the words "the number" and the words
"a number" by x.

>>...8 more than the square of x is 6 times x...<<

Replace the words "the square of x" by x² and the words "8 times x" by 8x

>>...8 more than x² is 6x...<<

Now to get 8 more than anything we write it down and then add 8 to it.
So to get 8 more than x², we write x² down and then add 8 to it.  When we
do that we get x² + 8.  So we replace the words "8 more than x²" by x² + 8

>>...x² + 8 is 6x...<<

Finally we replace the word "is" by an equal sign =.

    x² + 8 = 6x

Can you solve that? If not post again asking how.

Answer: There are two solutions, x = 2 and x = 4

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The length of a rectangle is 2 ft more than the width. the area is 42 sq. 
ft.  Find the width.

Let x be the width.

>>..the length of a rectangle is 2 ft more than the width...<<

So the length is x + 2  .

>>...the area is 42 ft find the width...<<

Area = length × width

42 = (x + 2)x

42 = x(x + 2)

Can you finish solving that?  If not post again asking how.

You'll have to use the quadratic formula because it won't factor.
                               __
You get two solutions, x = -1±Ö43
                                   __
Discard the negative solution, -1-Ö43, which is about -7.557438524
                                   __
Keep the positive solution x = -1+Ö43, which is about 5.557438524

So the width is about 5.557438524 and the length is 2 more, or
about 7.557438524

Checking: The area is (5.557438524)(7.557438524) = 41.99999785 which is
very close to 42.

Edwin