Solve the following problem for the roots by completing the square. 3x2 - 12x = 9

x = 2 ±√7

Step-by-step explanation:

Given in the question an expression,

3x² - 12x = 9

Let's assume that the expression can be factored as the perfect square (x+a) ²

This expression is expanded as x²+2ax+a²

Step1

divide by 3

3x²/3 - 12x/3 = 9/3

x² - 4x = 3

Step2

Add completing the square

2ax = - 4x

a = - 2

a² = 4

x² - 4x + 4 = 3+4

x² - 4x + 4 = 7

(x-2) ² = 7

Step3factor

(x-2) ² = 7

√ (x-2) ² = √7

x-2 = √7

x = 2 ±√7

X = - 1/4 or - 0.25 or - 2x2 (square)