What is the x equal too in x² - 3x = 54?

Well, we know standard form of quadratic equation : ax² + bx + c where,

a = Coefficient of x²

b = Coefficient of x

c = Constant term

We also equation for determinant :

⇒ b² - 4ac

Here, if value of determinant i.e. (b² - 4ac) = A perfect Square, then we can understand that the givdn equation is factorisable.

But, if the value of (b² - 4ac) ≠ A perfect square, then it will be considered as "Not factorisable"

Now let's calculate whether the equation is factorisable or not :

Comparing the given equation with ax² + bx + c, we get :

a = 1

b = -3

c = -54

Putting values in the determinant equation :

⇒ (-3)² - 4(1 × -54)

⇒ 9 + 216

⇒ 225

⇒ 15²

So, determinant = A perfect square

That means the given equation is factorisable.

Now let's factorize with by middle term splitting :

⇒ x² - 3x - 54

⇒ x² -(9 - 6)x - 54

⇒ x² - 9x + 6x - 54

⇒ x(x - 9) + 6(x - 9)

⇒ (x + 6)(x - 9) [Required Solution]

Hence, we get our required solution.

Hope this Helps (✿◡‿◡)