Seven less than the square of
a number is twice the sum of the same number and five
Replace the underlined words by the letter x. You get this:
Seven less than the square of x is twice the sum of x and five.
Now I'll underline some more words:
Seven less than the square of x is twice the sum of x and five.
Replace those underlined words by x². You get this:
Seven less than x² is twice the sum of x and five.
Now I'll underline some more words:
Seven less than x² is twice the sum of x and five.
Replace the underlined words by x+5. You get:
Seven less than x² is twice x+5.
Now I'll underline some more words:
Seven less than x² is twice x+5.
Replace the underlined words with 2(x+5). You get:
Seven less than x² is 2(x+5).
Now I'll underline some more words:
Seven less than x² is 2(x+5).
Replace the underlined words with x²-7.
[Notice that to make something "seven less" you subtract
"7 from it", you don't subtract "it from 7".]
You get:
x²-7 is 2(x+5).
Now I'll underline just one more word:
x²-7 is 2(x+5).
Replace that underlined word by =
x²-7 = 2(x+5)
Now the English has been translated into algebra
x²-7 = 2(x+5)
x²-7 = 2x+10
x²-17 = 2x
x²-2x-17 = 0
There are two solutions:
which is approximately 5.242640687
and
which is approximately -3.242640687
Edwin
