Fsc Part 1 Mathematics (Complete Solution)

Q12
Solve the following equations by completing the square

x2 - 3x - 648 = 0
x2 - 3x = 648
x2- 2(
3
2
)x = 648
Add (
3
2
)2 to both sides
x2- 2(
3
2
)x + (
3
2
)2= 648 + (
3
2
)2
(x -
3
2
)2= 648 +
9
4
(x -
3
2
)2=
4(648) + 9
4
(x -
3
2
)2=
2601
4
(x -
3
2
)2= (±
51
2
)2
Taking Square Root on both sides

x -
3
2
= ±
51
2
x = ±
51
2
+
3
2

Either     x =
51
2
+
3
2
     OR      x = -
51
2
+
3
2
x =
54
2
x = -
48
2
x = 27 x = -24

The Solution Set of the equation is {-24, 27}

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