(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)