Question

What equation results from completing the square and then factoring? x^2+22x=31 A.(x+22)^2=53 B.(x+22)^2=152 C.(x+11)^2=152 D.(x+11)^2=53

Answer 1

Answer:

$\boxed{\mathrm{Option \ C}}$

Step-by-step explanation:

=> $x^2+22x = 31$

=> $(x)^2+2(x)(11) = 31$

Since b = 11 , So $(11)^2$ needs to be added to both sides

Adding $(11)^2$  to both sides

=> $(x)^2+2(x)(11)+(11)^2 = 31+(11)^2$

Completing the square

=> $(x+11)^2 = 31+121$

=> $(x+11)^2 = 152$