Hi. My question is: x^2 + (2 root 7)x + 7 = 0 Solve the equation by factoring.

Question

Hello. Please help me with the above problem. I really need help. Thank you so much!

Answer 1

Note that

 

x² + (2√7)x + 7 = x² + (2√7)x + (√7)²

 

x² + (2√7)x + (√7)² = (x + √7)²

 

You actually have a perfect square.  So there is one root, x = -√7.

 

Answer 2

x²+2root7(x)+7=0

 

factor to 

 

(x+root7)(x+root7)=0

 

now solve for x

 

x=-root 7