Question

2x²+x-4=0 solve the method by completing the square​

Answer 1

Answer:

x = ±√( 33 / 16 ) - 1 / 4

Step-by-step explanation:

⇒ 2x^2 + x - 4 = 0

⇒ ( 2x^2 + x - 4 ) / 2 = 0

⇒ x^2 + ( x / 2 ) - ( 4 / 2 ) = 0

⇒ x^2 + ( x / 2 ) - 2 = 0

⇒ x^2 + 2( x / 4 ) - 2 = 0

⇒ x^2 + 2( x )( 1 / 4 ) - 2 = 0

⇒ x^2 + 2( x )( 1 / 4 ) + ( 1 / 16 ) - ( 1 / 16 ) - 2 = 0

⇒ x^2 + 2( x )( 1 / 4 ) + ( 1 / 4 )^2 - ( 1 / 16 ) - 2 = 0

⇒ ( x + 1 / 4 )^2 = 1 / 16 + 2           { a^2 + 2ab + b^2 = ( a + b )^2 }

⇒ ( x + 1 / 4 )^2 = ( 1 + 32 ) / 16

⇒ ( x + 1 / 4 )^2 = 33 / 16

⇒ x + 1 / 4 = √( 33 / 16 )

⇒ x = ±√( 33 / 16 ) - 1 / 4