Question

Rewrite the equation by completing the square.
x^{2}+10x+21 = 0
(x+__)^2=__

Answer 1

Answer:

Step-by-step explanation:

x²+10x+21=0

x²+10x+(10/2)²-(10/2)²+21=0

x²+10x+25-25+21=0

(x+5)²-4=0

(x+5)²=4

(x+y)²=(x+y)(x+y)=x(x+y)+y(x+y)=x²+xy+xy+y²=x²+2xy+y²

(x+y)²=x²+2xy+y²

coefficient of x=2y

y²=[(coefficient of x)/2]²=(2y/2)²=y²

Answer 2

(x+7)(x+3) would be the answer, but that not completing the square! 21 is not a proper square so it doesn’t work...
Is there an option for no solution?