Question

What number must you add to complete the square x^2+10x=0

A.25/2
B.25
C.5
D.3

Answer 1

B. 25

Explanation:

`(a+b)^2=a^2+2ab+b^2\\\\\text{We have}\\\\x^2+10x=0\\\\x^2+2(x)(5)=0\\\\\text{Therefore we have}\ a=x\ \text{and}\ b=5.\\\\\text{We need}\ b^2\to5^2.\\\\x^2+2(x)(5)=0\qquad\text{add}\ 5^2\ \text{to both sides}\\\\x^2+2(x)(5)+5^2=5^2\\\\(x+5)^2=25`