QUADRATIC EQUATIONS
Completing The Squares Method Contd….
Q) Solve the following quadratic equations by completing square.
i) z2 + 6z – 8 = 0
Sol:
z2 + 6z - 8 = 0
1
2) Constant on the RHS
∴ z2 + 6z = 8
…………(i)
3) Find the third term
Third term =
=
= (3)2
= 9
4) Add third term on both the sides
Adding ‘9’ on both sides of (i), we get
z2 + 6z = 8
+ 9 + 9
6
5) Express L.H.S. in square form.
∴ z
To express LHS
in square form
Take square root of 1st term
Take square root of 3rd term
3
+
Take middle term sign
( ) 2
Make it whole square
= 17
6) Take square root & write the solution
Taking square roots on both sides
∴ z + 3 =
∴ z = - 3
∴ z =
or
z =
1) Coefficient of square term should be 1
STEPS
Coefficient of 1st term is 1
ii) x(x – 1) = 1
Sol:
x(x – 1) = 1
∴ x2 – x = 1
1
…………(i)
Third term =
=
- 1
1
=
x2 – x = 1
To express LHS
in square form
Take square root of 1st term
Take square root of 3rd term
Take middle term sign
Make it whole square
∴ x
–
( )2
Taking square roots on both sides
Q) Solve the following quadratic equations by completing square.
STEPS
1) Coefficient of first term should be 1
2) Constant on the RHS
3) Find the third term
4) Add third term on both the sides
5) Express L.H.S. in square form.
6) Take square root & write the solution