\(x2 + 10x + 25\)
First we can rewrite 25 to 52 and we will check the middle term by multiplying 2ab. This is factoring by the perfect square rule. Now we can check the result of this new problem compared to the original expression.
We now have \(2ab = 2*x*5 = 0\)
Simplify this to \(2ab = 10x =0\)
Now we factor by the perfect square trinomial rule [ \(a2+2ab+b2=(a+b)2a2+2ab+b2=(a+b)2\) where \( a=xa=x \) and \(b=5b=5.\) ] to get: \(( x + 5 ) 2 = 0\).
Next we can set \(x+5\) equal to 0 and solve for \(x \).
Set the factor equal to 0 and we get: \(x+5=0\)
Solve that and you get x = -5