How do you solve using the completing the square method #7x²+9x+1=0 #?

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Answer 1 · 2018-03-03T07:04:49

#color(green)(x = -1.5429, -2.9571#

#7x^2 + 9x + 1 = 0#

#cancel7(x^2 + (9/7)x + (1/7)) = 0#

#(x^2 + (2 * (9/14) x) = -(1/7)#

Add #(9/14)^2# to both sides.

#x^2 + (2 * (9/14) x) + (9/14)^2 = -1/7 + 9 / 14 = 1/2#

#(x+ 9/14))^2 = (sqrt (1/2))^2#

#x + (9/4) = +- sqrt (1/2)#

#x = +sqrt(1/2) - (9/4), -sqrt(1/2) - (9/4)#

#color(green)(x = -1.5429, -2.9571#