Question

2x^2+x-4 by completing squarre method

Answer 1

hi!!

here's ur answer...

given :- 2x² + x - 4

=> x² + x/2 - 2 = 0

=> (x + 1/4)² - (1/4)² - 2 = 0

=> (x + 1/4)² - 1/16 - 2 = 0

=> (x + 1/4)² -33/16 = 0

=> (x + 1/4)² = 33/16

=> x + 1/4 = ± √33/4

=> x = -1/4 ± √33/4

x = (-1 + √33)/4 or x = (-1-√33/4)

hope this helps..!!

Answer 2

Given Equation is 2x^2 + x - 4 = 0.

It can be written as :

= > x^2 + (x/2) - (4/2) = 0

= > x^2 + (x/2) - 2 = 0

Adding and subtracting (1/4)^2, we get

= > x^2 + (x/2) - 2 + (1/4)^2 - (1/4)^2 = 0

= > x^2 + (x/2) + (1/4)^2 - 2 - (1/4)^2 = 0

= > (x + 1/4)^2 - 2 - (1/4)^2 = 0

= > (x + 1/4)^2 = 2 + (1/4)^2

= > (x + 1/4)^2 = 2 + (1/16)

= > (x + 1/4)^2 = 33/16

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(1)

$= > x + \frac{1}{4} = \sqrt{\frac{33}{16}}$

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

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

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

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(2)

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

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

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

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Therefore, The values are:

$= > Answer : \boxed { x = \frac{\sqrt{33} - 1}{4}, \frac{-\sqrt{33} - 1}{4}}}$

Hope this helps!