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