Simplify: 10x2+20x=9-71=-62
To solve by completing the square:
Divide through by 10: x2+2x=-6.2
Complete the LHS square: x2+2x+1=-6.2+1 (1 has to be added to RHS as well to preserve equality)
We have a perfect square on the left:
(x+1)2=-5.2 which cannot be solved for real numbers because no perfect square can be negative. This suggest an error in the question. For a solution the RHS must be positive.
If the quadratic had been 10x2+20x-71=9, then:
10x2+20x=80
x2+2x=8 after dividing through by 10
Complete the square:
x2+2x+1=8+1=9
(x+1)2=9
x+1=3 or -3 making x=2 or -4.
[The equation becomes 10(x2+2x-8)=0, which factorises 10(x-2)(x+4)=0]