Question

Solve the quadratic equation by completing the square and applying the square root property.

Answer 1

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:

`\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}`

Hence, the answer is option d