Question

What must be added to 25x2 +60x + 12 to make it as a perfect square?

Answer 1

Look for the clues as described below.
Step-by-step explanation:
If the trinomial is a perfect square trinomial, there will be some properties to check for.
a
x
2
±
b
x
+
c

both
a
and
c
must be perfect squares, with plus signs
check whether
b
=
2
×
√
a
×
√
c

In this case:
a
=
25
=
5
2

and
c
=
36
=
6
2

2
×
√
25
×
√
36
=
2
×
5
×
6
×
=
60

b
=
60

Therefore we know that
25
x
2
−
60
x
+
25
is the square of a binomial.
It will factorise as:
25
x
2
−
60
x
+
25
=
(
5
x
−
6
)
2

Answer 2

`(36)/(25)`

Step-by-step explanation:

25
`x^(2)` + 60x = -12 Divide all the way through by 25

`(25x^(2) )/(25)` +
`(60x)/(25)` =
`(-12)/(25)`

`x^(2)` +
`(12x)/(5)` =
`(-12)/(25)`

`((12)/(5) x(1)/(2)) ^(2)`

`((12)/(10)) ^(2)` =
`((6)/(5)) ^(2)` =
`(36)/(25)`

Helping in the name of Jesus.