Find the error, Rashid and Tia solve the quadratic equation (2x2-8x +10=0) by completing the square. Who is correct? Explain your reasoning.

Rashid Tia
2x^2−8x+10=0 2x^2−8x+10=0
2x^2−8x=−10 x^2−4x=0−5
2x^x−8x+16= −10+16 x^2−4x+4=−5+4
(x−4)^2=6 (x−2)^2= −1
x− 4=±6√ x−2=±i
x= 4±√6 x=2±i

Question

Find the error, Rashid and Tia solve the quadratic equation (2x2-8x +10=0) by completing the square. Who is correct? Explain your reasoning.

Rashid	                                        Tia
2x^2−8x+10=0	               2x^2−8x+10=0                         
2x^2−8x=−10	                      x^2−4x=0−5
2x^x−8x+16= −10+16	     x^2−4x+4=−5+4
(x−4)^2=6                              (x−2)^2= −1
x− 4=±6√	                      x−2=±i
x= 4±√6	                              x=2±i

solomonzelman · Answer

Hint:   In line 3, the error lays.

solomonzelman · Answer

Which one is, and which is NOT a perfect square trinomial?

2x^x−8x+16    or    x^2−4x+4   ?

calculusxy · Answer

In completing the square, it is essential to make sure that the $a$ value of the quadratic equation is equal to 1. Therefore, typically people divide every coefficient with the $a$ value in order to make sure that $a = 1$. I believe that only one of the two does this.