Fsc Part 1 Mathematics (Complete Solution)
Q13
Solve the following equations by completing the square
x2 - x - 1806 = 0
x2 - x = 1806
x2- 2(
)x = 1806
1 |
2 |
Add (
)2 to both sides
1 |
2 |
x2- 2(
)x + (
)2= 1806 + (
)2
1 |
2 |
1 |
2 |
1 |
2 |
(x -
)2= 1806 +
1 |
2 |
1 |
4 |
(x -
)2=
1 |
2 |
4(1806) + 1 |
4 |
(x -
)2=
1 |
2 |
7225 |
4 |
(x -
)2= (±
)2
1 |
2 |
85 |
2 |
Taking Square Root on both sides
x -
= ±
1 |
2 |
85 |
2 |
x = ±
+
85 |
2 |
1 |
2 |
Either | x =
|
OR | x = -
|
||||||||
x =
|
x = -
|
||||||||||
x = 43 | x = -42 |
The Solution Set of the equation is {-42, 43}