How to solve 5x2+20x+13=0 by completing the square?

2 Answers
maganbhai P.
Mar 1, 2018

x=−10±√355

Explanation:

5x2+20x+13=0
Multiplying both sides by 5, we get
25x2+100x+65=0
⇒25x2+2(5x)(10)+100−35=0
⇒(5x)2+2(5x)(10)+(10)2−35=0
⇒(5x+10)2−35=0
⇒(5x+10)2=35=(√35)2
⇒5x+10=±√35
5x=−10±√35
x=−10±√355

Sahar Mulla ❤
Mar 2, 2018

5x2+20x+13=0

15(x2+4x+135)=0

x2+4x+135=0

Now, add and subtract, half of the x-term squared, i.e. (42)2=22=4

⇒[x2+4x+4]+[135−4]=0

⇒[x2+4x+22]=[4−135]

⇒(x+2)2=205−135

⇒(x+2)=±√75

⇒x=−2±√75

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