Question

Find the root by factrisation2x^2-x+1/8=0

Answer 1

Greetings,
 The answer to your question is typed below ^
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Given:

2x² - x + 1/8 = 0

Solution:
First we multiply each term by 8 to make calculations easier.
we get:
(2x²)8 - (x)8 + (1/8)8 = 0

⇒ 16x² - 8x + 1=0
⇒ 16x² - 4x - 4x + 1 = 0 ( by splitting the middle term -8x as -4x and -4x)
⇒ 4x(4x - 1) - 1 ( 4x - 1) = 0 ( here take 4x and -1 common)
⇒ (4x - 1) (4x - 1)=0

⇒ x = 1/4    or  x = 1/4

Ans.:    x = 1/4 or 0.25
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We can also use the b²-4ac method:

we take the  equation 16x² - 8x +1 =0
Then take the coefficients of x², x and the last term
as
a = 16 , b = -8 , c = 1

according to the formula  x = (-b +/- √(b² - 4 a c)) / 2a

∴  x = ( 8 +/- √ (64 - 4 * 16 * 1)) / 2 * 16
⇒ x= ( 8 +/- √(64 -64) ) /  32
⇒ x = ( 8 +/- 0) / 32
x= ( 8 + 0 ) /32                   or                x= ( 8 - 0 ) / 32
x = 1/4                               or               x = 1/4

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PS.: Enjoy ;)