Question

How do you factor $9{x^2} - 36x + 36 = 0$ ?

Answer 1

Hint: To solve this we have to know about algebraic identity.
Quadratic equation: a polynomial equation in which the highest sum of exponents of a variable in any term is two. The value of $x$ for which the result of the equation is zero then that value will be the root of the quadratic equation.

Complete step by step answer:
To solve this question. We will first factorize it:
We try to take common from the given equation $9{x^2} - 36x + 36 = 0$ .
Let’s divide the whole equation by $9$ . We get,
 $\dfrac{9}{9}{x^2} - \dfrac{{36}}{9}x + \dfrac{{36}}{9} = 0$
We get,
 ${x^2} - 4x + 4 = 0$
Splitting the equation. We get,
 ${x^2} - 2.2.x + {2^2} = 0$
By using ${(a - b)^2} = {a^2} + {b^2} - 2ab$
We get,
 ${x^2} - 2.2.x + {2^2} = {(x - 2)^2}$

Note: To calculate it root we can do:
Hence LHS is equal to zero so, we can conclude that either,
 $\left( {x - 2} \right) = 0$
So, we will get,
 $\left( {x - 2} \right) = 0$
 $ \Rightarrow x = 2$