We can write the given equation as follow:
2x^2 - 9x + 6 = 0
To complete the square we can first multiply the equation by 8:
16x^2 - 72x + 48 = 0
Next, we can add 33 both sides:
16x^2 - 72x + 48 + 33 = 33
16x^2 - 2*4*9 + 81 = 33
The left side of the previous equation is a perfect square, then:
(4x - 9)^2 = 33
Now, by applying the square root property, that is, by applying square root both sides, we get:
4x - 9 = ± √33
By solving for x we obtain:
[tex]\begin{gathered} x=\frac{9\pm\sqrt[\placeholder{⬚}]{33}}{4} \\ x=\lbrace\frac{9-\sqrt[\placeholder{⬚}]{33}}{4},\frac{9+\sqrt[\placeholder{⬚}]{33}}{4}\rbrace \end{gathered}[/tex]
Hence, the answer is option d
