Question

solve the following quadratic equation by completing the square : 2x²+ x + 4 = 0​

Answer 1

The given quadratic equation is
2x
2
+x−4=0
⇒x
2
+
2
x
​
−2=0
⇒x
2
+
2
x
​
=2
On adding both sides
16
1
​
we get
x
2
+
2
x
​
+
16
1
​
=2+
16
1
​

⇒(x+
4
1
​
)
2
=
16
33
​

⇒x+
4
1
​
=±
4
33
​

​

⇒x=±
4
33
​

​
−
4
1
​

⇒x=
4
−1−
33
​

​
,
4
−1+
33
​

​

Answer 2

Answer:

Giving Answer -

${2x}^{2} + x - 4 = 0$

$= {x}^{2} + \frac{x}{2} - 2 = 0$

$= {x}^{2} + \frac{x}{2} = 2$

$on \: adding \: both \: sides \: by \: \frac{1}{16} \: we \: get$

${x}^{2} + \frac{x}{2} + \frac{1}{16} = 2 + \frac{1}{16}$

$= > (x + \frac{1}{4} )^{2} = \frac{33}{16}$

$= > x + \frac{1}{4} = \frac{ \sqrt{33} }{4}$

$= > x = \frac{ \sqrt{33} }{4} - \frac{1}{4}$

$= > x = \frac{ - 1 - \sqrt{33} }{4} \: \frac{ - 1 + \sqrt{33} }{4}$

Thank You

$we \: value \: your \: care$