How do you solve using the completing the square method #10x^2 = 4x + 7#?

2 Answers

Answer:

#x_1=(2+sqrt(74))/10 and x_2=(2-sqrt(74))/10#

Explanation:

#10x^2=4x+7#

#10x^2-4x-7=0#

#100x^2-40x-70=0#

#100x^2-40x+4-74=0#

#(10x-2)^2-(sqrt(74))^2=0#

#(10x-2)^2=(sqrt(74))^2#

Hence #x_1=(2+sqrt(74))/10# and #x_2=(2-sqrt(74))/10#

Jul 9, 2017

Answer:

#x = 1/5 +- sqrt(37/50)#

Explanation:

#10x^2 - 4x = 7#
Divide both sides by 10:
#x^2 - (4x)/10 = 7/10#
#x^2 - (2x/5) = 7/10#
#(x^2 - (2x)/5) + 1/25 = 7/10 + 1/25#
#(x - 1/5)^2 = 37/50#
#(x - 1/5) = +- sqrt(37/50)#
#x = 1/5 +- sqrt(37/50)#