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

2 Answers
Cem Sentin ยท Stefan V.
Jul 9, 2017

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

Nghi N
Jul 9, 2017

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)

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