How do you solve using the completing the square method 10x^2 = 4x + 710x2=4x+7?

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

x_1=(2+sqrt(74))/10 and x_2=(2-sqrt(74))/10x1=2+√7410andx2=2−√7410

Explanation:

10x^2=4x+710x2=4x+7

10x^2-4x-7=010x2−4x−7=0

100x^2-40x-70=0100x2−40x−70=0

100x^2-40x+4-74=0100x2−40x+4−74=0

(10x-2)^2-(sqrt(74))^2=0(10x−2)2−(√74)2=0

(10x-2)^2=(sqrt(74))^2(10x−2)2=(√74)2

Hence x_1=(2+sqrt(74))/10x1=2+√7410 and x_2=(2-sqrt(74))/10x2=2−√7410

Nghi N
Jul 9, 2017

x = 1/5 +- sqrt(37/50)x=15±√3750

Explanation:

10x^2 - 4x = 710x2−4x=7
Divide both sides by 10:
x^2 - (4x)/10 = 7/10x2−4x10=710
x^2 - (2x/5) = 7/10x2−(2x5)=710
(x^2 - (2x)/5) + 1/25 = 7/10 + 1/25(x2−2x5)+125=710+125
(x - 1/5)^2 = 37/50(x−15)2=3750
(x - 1/5) = +- sqrt(37/50)(x−15)=±√3750
x = 1/5 +- sqrt(37/50)x=15±√3750

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