How do you solve the equation #x^2+x+1/4=9/16# by completing the square?

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Answer 1 · 2017-01-27T09:14:43

#x=1/4" or "-5/4#

rearrange as follows

#x^2+x=9/16-1/4#

#x^2+x=5/16#

complete the square #LHS#

#(x^2+x+(1/2)^2)-(1/2)^2=5/16#

#(x+1/2)^2-1/4=5/16#

now solve for #x#

#(x+1/2)^2=5/16+1/4=9/16#

#(x+1/2)^2=9/16#

#x+1/2=+-sqrt(9/16)#

#x+1/2=+-3/4#

#x=-1/2+-3/4#

#x_1=-1/2+3/4=1/4#

#x_2=-1/2-3/4=-5/4#