Answer:
a = 3, -17
Explanation:
a ² + 14a - 51 = 0
1) put the a, not a ², in parenthesis.
2) half the coefficient (14) of a. that is 7. Put that into same parenthesis.
3) we have (a + 7)
4) square this and multiply out. (a + 7) ² = a ² + 7a + 7a +49 = a ² +14a + 49
5) this looks just like the original equation except for +49. What do we have to do to get back to original? 49 – (-51) = 49 + 51 = 100. We have to subtract 100
6) now we have (a + 7) ² – 100 =0
7) (a + 7) ² = 100
8) (a + 7) = ± √100
9) a = ± √100 - 7
a = ±10 - 7
= -17 and 3