Question

Solve the following quadratic equations by completing the squares method.
(i) 2x²+x-4=0
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Answer 1

Answer:

2x^2 +x-4 =0

dividing the equation by 2

2x^2 /2 +x/2 - 4/2=0

x^2 +x/2 ‐ 2=0

x^2 +x/2 =2

multiplying the mid term with 1/2

1/2×1/2=1/4

adding the square to both the sides

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

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

(x+1/4)^2=32+1/16

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

x+1/4=+-_/33/16

x+1/4=+‐_/33/4

x=_/33/4‐1/4=_/33‐1/4

or

x=‐_/33/4‐1/4=-_/33-1/4

so the two roots are

root 33-1/4 and another one is ‐root 33‐1/4

hope this will help you

Answer 2

Answer:

2(x2+x/2-2)=0

coefficient of x =1/2

half of coefficient of x =1/2*1/2=1/4

(half)^2=(1/4)^2=1/16

now put 1/16 in both sides of equation

x2+x/2+1/16=2+1/16

(x+1/4)^2=32+1/16

x+1/4=√33/16

x+1/4=±√33/4

x=-1/4+√33/16‚x=-1/4-√33/16

answer is .

x=-4+√33/16‚ x=-4+√33/16