Question

For which equation does it make the most sense to solve by completing the square?

Answer 1

First equation is $x^{2} -8 = 1$ , subtract 1 from both sides , we get

$x^{2} -9=0$

This can easily be solved using Difference of Two Squares.

Second is $3x^{2} -x+17=0$ , As here the leading coefficient is 3 , it means to apply Completeing the squares , we have to divide all terms by 3 , and we will get fractions , and it will become complex , So better to solve this using using Quadratic formula.

Third is $5x^{2} +3x = 9$

Here also the leading coefficient is 5 and we have to divide by 5 , all terms to apply Completing the squares , again we will get fractions , so it will become complex, so better to solve it using Quadratic formula.

Fourth is $x^{2} +20x=52$

This is a perfect equation to solve it using Completing the squares, as here the leading coefficient is already 1 ,

So fourth equation is the best one to solve using Completing the squares

Answer 2

The last equation is the most suitable one to be solved by completing the square .