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
2x^2−8x+10=0
2x^2−8x=−10
2x^x−8x+16=−10+16
(x−4)2=6
x−4=±6–√
x=4±6–√

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

Answer 1

To solve a quadratic equation using completing the square method,
STEP 1
Divide through by the coefitient of the squared term.

Looking at the solutions of Rashid and Tia, we notice that Rashid did not divide through by the coefficient of $x^2$.

Therefore, Rashids solution is wrong.

We solve the equation using completeing the square as follows:
$2x^2-8x+10=0 \\ \\ x^2-4x=0-5=-5 \\ \\ x^2-4x+4=-5+4=-1 \\ \\ (x-2)^2=-1 \\ \\ x-2=\pm i \\ \\ x=2\pm i$