How do you solve x^2 - 8x + 3 = 0x2−8x+3=0?
1 Answer
Apr 30, 2016
Explanation:
Complete the square and use the difference of squares identity:
a^2-b^2=(a-b)(a+b)a2−b2=(a−b)(a+b)
with
0 = x^2-8x+30=x2−8x+3
=(x-4)^2-16+3=(x−4)2−16+3
=(x-4)^2-13=(x−4)2−13
=(x-4)^2-(sqrt(13))^2=(x−4)2−(√13)2
=((x-4)-sqrt(13))((x-4)+sqrt(13))=((x−4)−√13)((x−4)+√13)
=(x-4-sqrt(13))(x-4+sqrt(13))=(x−4−√13)(x−4+√13)
So:
x = 4+-sqrt(13)x=4±√13
