Question

Complete the square to solve the equation below

x^2+x=7/4

A. x=-2+√2 ; x=-2 - √2
B. x=-1/2+√2 ; x=-1/2- √2
C. x=3 ; x=-1
D. x=1+√2 ; x=1- √2

Answer 1

`x^2+x= (7)/(4)`

Take one-half of the coefficient of x and square it, then add it to both sides.


`x^2+x+ ((1)/(4)) =(7)/(4)+ ((1)/(4))`


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


`\left(x+(1)/(2)\right)^2=2`


`x+(1)/(2)=\pm √(2)`
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`x+(1)/(2)=- √(2)`

`x=-(1)/(2)- √(2)` <=

AND


`x+(1)/(2)= √(2)`

`x= √(2)-(1)/(2)` <=