Gmat_mission wrote:If \(x−5=\sqrt{2x^2−18x+37} \) then \(x\) could equal

A. 2
B. 3
C. 4
D. 5
E. 6

[spoiler]OA=E[/spoiler]

Source: Magoosh

Hi Gmat_mission. Here is how I would solve it.

The right-hand side is a square root, then it is greater than or equal to zero. Therefore, the left-hand side has to be greater than or equal to zero.
With this, we can discard the options: A, B and C.

To know which of the remaining two options is the correct one, let's plug x=5 into the equation and see if we get a true statement. $$x-5=\sqrt{2x^2−18x+37}$$ $$5-5=\sqrt{2\cdot5^2-18\cdot5+37}$$ $$0=\sqrt{50-90+37}$$ $$0=\sqrt{-3}$$ Here, we've got a false statement, therefore, we also discard the option D.

In conclusion, the correct answer is the option _E_.

I hope it helps you. <i class="em em-sunglasses"></i>