How to factorise an expression which doesn't factorise over the integers?

Question

How can I factorise this expression:

$$x^2+58x+100$$

I got an answer and I don't know if it's correct:

$(x+\surd 741 -2a)(x-\surd 741 -2a)$.

Answer 1

I think that $2a$ should be $29$ and the sign should be positive (if the roots of the equation are $a,b$ the factorisation is $(x-a)(x-b)$)

Check sum of negatives of roots $(29+\sqrt {741})+(29-\sqrt {741})=58$

Check product of roots $(29+\sqrt {741})(29-\sqrt {741})=29^2-741=100$

Answer 2

Is "$2a$" a typo? If not,it should be $(x+29-\sqrt{741})(x+29+\sqrt{741})$.

Using completing square method,

\begin{align} x^2+58x+100&=(x+29)^2-29^2+100\\&=(x+29)^2-741\\&=(x+29-\sqrt{741})(x+29+\sqrt{741}) \end{align}

If yes and you meant $-29$, you still get it wrong as it should be$+29.$