Question

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

Answer 1

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

Answer 2

Answer:

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;

$x-6 = \pm \sqrt{90}$

Add 6 to both sides we have;

$x = 6\pm \sqrt{90}$

or

$x = 6 \pm 3\sqrt{10}$

Therefore, the value of x are:

$6+3\sqrt{10}$ and $6-3\sqrt{10}$