Question

How do you solve $ {x^2} - 6x + 6 = 0 $

Answer 1

Hint: In this question, we are given a quadratic equation and we have to find the factors. The quadratic equation had two factors. Find the factors by the formula that $ \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} $ where $ a{x^2} + bx + c = 0 $ is a quadratic equation.

Complete step-by-step answer:
In this question, we had a trinomial expression and we had to find the factors for this expression. Trinomial is the math equation having three terms which are connected through the plus or minus notations.
The given expression is $ {x^2} - 6x + 6 = 0 $ a quadratic equation.
Compare the quadratic equation with $ a{x^2} + bx + c = 0 $
 $ a = 1,b = - 6,c = 6 $
Finding the factors by putting these values into the formula
 $ \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}} $
Factors are
$ \dfrac{{ - \left( { - 6} \right) \pm \sqrt {{{\left( { - 6} \right)}^2} - 4\left( 1 \right)\left( 6 \right)} }}{{2\left( 1 \right)}} $
So, the factors are
$ \dfrac{{6 \pm \sqrt {36 - 24} }}{2} = \dfrac{{6 \pm \sqrt {12} }}{2} $
 $ \dfrac{{6 \pm 2\sqrt 3 }}{2} = \dfrac{{3 \pm \sqrt 3 }}{1} $
The required factors are $ 3 + \sqrt 3 ,3 - \sqrt 3 $
This is our required solution.
So, the correct answer is “ $ 3 + \sqrt 3 ,3 - \sqrt 3 $ ”.

Note: The factors can be found by splitting the middle term method too. But in some questions like the above we are unable to find the factors. So, we used the formula for finding the factors. Apply the formula properly.