Fsc Part 1 Mathematics (Complete Solution)

Q13
Solve the following equations by completing the square

x2 - x - 1806 = 0
x2 - x = 1806
x2- 2(
1
2
)x = 1806
Add (
1
2
)2 to both sides
x2- 2(
1
2
)x + (
1
2
)2= 1806 + (
1
2
)2
(x -
1
2
)2= 1806 +
1
4
(x -
1
2
)2=
4(1806) + 1
4
(x -
1
2
)2=
7225
4
(x -
1
2
)2= (±
85
2
)2
Taking Square Root on both sides

x -
1
2
= ±
85
2
x = ±
85
2
+
1
2

Either     x =
85
2
+
1
2
     OR      x = -
85
2
+
1
2
x =
86
2
x = -
84
2
x = 43 x = -42



The Solution Set of the equation is {-42, 43}

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