Question

Solve for x
in the equation x^2-12x+36=90

Answer 1

Using the identity rule:

`(a-b)^2 = a^2-2ab+b^2`

Given the equation:

`x^2-12x+36 = 90`

Rewrite the above equation as:

`x^2-2 \cdot x \cdot 6+6^2 = 90`

Apply the identity rule:

`(x-6)^2 = 90`

Take square root to both sides we have;

`x-6 = \pm √(90)`

Add 6 to both sides we have;

`x = 6\pm √(90)`

or

`x = 6 \pm 3√(10)`

Therefore, the value of x are:

`6+3√(10)` and
`6-3√(10)`

Answer 2

This can be rewritten as
(x -6)² = 90 . . . . . the left side is already a perfect square
x -6 = ±√90 . . . . . take the square root
x = 6 ±3√10 . . . . add 6