How do you solve 25x^2-50?

Question

(5x-5)(5x+10)?

I can't figure this one out.

Please Help!

Answer 1

 

(5X - 5)(5X + 10)        Would give you:

= (5X)×(5X) + (5X)×10 - 5×(5X) - 5×10

= 25X² + 50X - 25X - 50

= 25X² + 25X - 50

 

So since this isn't    25X² - 50 ,  (5X - 5)(5X + 10) can't be the correct answer.

 

So consider:

25X² - 50

For this equation we can take out a common factor of 25:

25X² - 50 = 25(X² - 2)

 

Now you can use the equation:

X = (- b ± (√ (b ² - 4 a c) ) / 2 a

 

For an equation in the standard form:

aX² + bX + c

 

So since for your equation,     25(X² - 2)    :

a = 1       ,       b = 0           , c = - 2

 

X = (- 0 ± √ (0 ² - 4 ×1×(-2) )) / (2 × 1)

X = ± √ (- 4×(-2) ) / 2

X = ± (√8) / 2

X = ± (√4×√2) / 2 = ± (2×√2) / 2 = ± √2

So the solution to your equation,      25(X² - 2)  :

 

25(X² - 2) = 25(X + √2)(X - √2)