3x^2 - 5x + 2 = 0 by completing the square method.
Answers
Answer:
Given 3x
2
−5x+2=0
Here, the coefficient of x
2
is 3 and it is not a perfect square.
∴ Multiply the equation throughout by 3.
⇒(3x
2
−5x+2=0)×3∴9x
2
−15x+6=0
Now, half of the coefficient of x is
2
5
.∴b=
2
5
and b
2
=(
2
5
)
2
So, 9x
2
−15x+(
2
5
)
2
−(
2
5
)
2
+6=0,(3x)
2
−15x+(
2
5
)
2
=(
2
5
)
2
−6
(3x−
2
5
)
2
=
4
25
−6=
4
1
(Taking square root on both the sides)
∴3x−
2
5
=±
2
1
∴3x−
2
5
=±
2
1
or 3x−
2
5
=−
2
1
3x=
2
1
+
2
5
3x=
2
5
−
2
1
3x=
2
6
=3 3x=
2
4
=2
∴x=1 x=
3
2
Answer:
x = 1, -2/3
Step-by-step explanation:
The given equation is not in the form to apply the method of completing squares. The coefficient of x2 is not 1.
To make the coefficient 1, we need to divide the whole equation by 3.
x2 – 5/3 x + 2/3 = 0
Comparing with the standard form of the equation
Stand form of equation is
ax2 + bx + c = 0, where a,b and c are real numbers such that a ≠ 0 and x is a variable.
b = -5/3; c = ⅔
c – b2/4 = ⅔ – [(5/3)2/4] = ⅔ – 25/36 = -1/36
So,
(x – 5/6)2 = 1/36
(x – 5/6)= ± √(1/36)
x – 5/6 = ±1/6
x = 1, -2/3