A^2+14a-51=0 solve the quadratic by completing the square.

A^2+14a-51=0
Add 51 to both sides
a^2+14a-51+51=0+51
a^2+14a=51
add (14/2)^2
a^2+14a+(14/2)^2=100
Solve a+7=+sqrt 100: a=3
Solve a-7 = -sqrt 100: a=-17
a=3 a=-17

Steps if you have ax^2+bx+c=0
1. put vairable on other side (-c from both sides)
2. make sure that leading term is 1 (ax^2+bx+c=0 where a=1)
3. take half of  b and square it

so
a^2+14a-51=0
move c to other side
add 51 to both sides
a^2+14a=51
leading term is 1
take 1/2 of b and square
14/2=7, 7^2=49
add that to both sides
a^2+14a+49=51+49
factor perfect square
(a+7)^2=100
square root both sides
a+7=+/-10

a+7=10
a+7=-10

a+7=10
minus 7
a=3

a+7=-10
subtract 7
a=-17

a=3 or -17