Question

solve 2x^2+x-4=0 by completing the square method

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Answer 1

2x²+x-4⇒ 2x² + x = 4

Dividing both sides of the equation by 2, we get

⇒ x⁴ +x/2 = 2

Now on adding (1/4)2 to both sides of the equation, we get,

⇒ (x)² + 2 × x × 1/4 + (1/4)² = 2 + (1/4)²

⇒ (x + 1/4)² = 33/16

⇒ x + 1/4 = ± √33/4

⇒ x = ± √33/4 – 1/4

⇒ x = ± √33-1/4

Therefore, either x = √33-1/4 or x = -√33-1/4

Answer 2

Answer:

 

2x2+x−4=02x2+x-4=0

⇒ 4x2+2x−8=0 [multiplying both sides by 2]⇒ 4x2+2x-8=0 [multiplying both sides by 2]

⇒ 4x2+2x=8⇒ 4x2+2x=8

⇒ (2x)2+2×2x×12+(12)2=8+(12)2⇒ (2x)2+2×2x×12+(12)2=8+(12)2

 [adding (12)2 on both sides][adding (12)2 on both sides]

⇒ (2x+12)2=(8+14)=334=(33−−√2)2⇒ (2x+12)2=(8+14)=334=(332)2

⇒ 2x+12=±(33−−√2)