Question

if i subtract 20 from my number, then square the result, i get the same answer as, if i square my number, then subtract 20 from the result

Answer 1

`\textrm{The number is: }\\\\\\ \rm{\boxed{(21)/(2)}\; or\; \boxed{10.5} \;in \;decimal}}`

Explanation:

Let x be the number we have to determine

From the question description

`\left(x-20\right)^2=\:x^2-20`

• 
  `\mathrm{Expand\:}\left(x-20\right)^2:\quad x^2-40x+400`
  The above uses the fact that (x- a)² = x² -2ax + a² with a = 20

• Set this equal to x² - 20:
  
  `x^2-40x+400 = x^2 - 20\\\\`
• Subtract x² from both sides:
  
  `x^2-40x+400 - x^2 = x^2 - 20 - x^2\\\\`
  
  `-4x + 400 = -20`
• Subtract 400 from both sides:
  
  `-40x + 400 - 400 = -20 - 400\\-40x = -420\\\\`
• Divide both sides by 40:
  
  `(-40x)/(-40)=(-420)/(-40)`
  
  `x = (21)/(2)`

Answer:

`\rm{\boxed{x = (21)/(2)}\; or\; \boxed{x = 10.5} \;in \;decimal}}`

Answer 2

The number is 10.5.

Explanation:

Let x be your number.

"i subtract 20 from my number,:" (x-20)

"square the result" : (x-20)^2

-------

"i square my number": x^2

"subtract 20 from the result": x^2 - 20

-----

The results are equal:

(x-20)^2 = x^2 - 20

x^2 -40x + 400 = x^2 - 20

-40x = -420

x = 10.5

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CHECK:

1) (x-20)^2 = ?

(10.5-20)^2 = 90.25

2) x^2 - 20 = ?

(10.5)^2 - 20 = 90.25

x=10.5 is correct