Question

ǫᴜᴇsᴛɪᴏɴ :

ғɪɴᴅ ᴛʜᴇ ʀᴏᴏᴛs ᴏғ
$4 {x}^{2} + 3x \: + 5 \: = \: 0$
ʙʏ ᴛʜᴇ ᴍᴇᴛʜᴏᴅ ᴏғ ᴄᴏᴍᴘʟᴇᴛɪɴɢ ᴛʜᴇ sǫᴜᴀʀᴇ.


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Answer 1

Answer:

x=(-3+_√-71)/8

Step-by-step explanation:

4x²+3x+5=0

=(2x)²+2(2x)3/4+9/16+71/16=0

$x {}^{2} {+ y }^ {2} + 2xy = (x + y) {}^{2}$

so,

(2x)²+2(2x)3/4+9/16+71/16=0

=(2x+3/4)²+71/16=0

=(2x+3/4)²=-71/16

apply root on both sides

√(2x+3/4)²=√-71/16

=2x+3/4=+_√-71/4 (√16=4)

2x=(-3+_√-71)/4

x=(-3+_√-71)/8