How do you solve using the completing the square method #x^2+x=7/4#?

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Answer 1 · 2017-03-19T05:51:42

#x=0.91421356 or x=-1.91421356#

#color(red)(Commenci ng)# #color(red)(compl e ti ng)# #color(red)(the)# #color(red)(squ are)# #color(red)(method)# #color(red)(now,)#

1) Know the formula for the perfect quadratic square, which is,

#(ax+-b)^2 = ax^2+-2abx+b^2#

2) Figure out your #a and b# values,

#a=# coefficient of #x^2#, which is #1#.
#color(red)(b=(1)/(2(1)) = 1/2)#

3) Add #color(red)(b^2)# on both sides of the equation, giving you an overall net of 0, hence not affecting the result of the equation,

#x^2+x+color(red)((1/2)^2)=7/4+color(red)((1/2)^2)#
#(x+1/2)^2=2#

4) Square root both sides,

#x+1/2=+-sqrt(2)#

5) Subtract #1/2# on both sides,

#x=+-sqrt2-1/2#

6) Calculate the two values of #x#,

#x=0.91421356 or x=-1.91421356#