4x^2-12x+5=0 Solve by completing the square

Question

Solve by completing the square 4x^2-12x+5=0.

Answer 1

Given equation 4x^2-12x+5= 0

Separate variables and constants aside by subtracting 5 from each side.

4x^2-12x = -5

Here x² coefficient is 4, for perfect square make x² coefficient 1 by dividing each side by 4.

x^2-3x = -5/4

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

x^2-3x+9/4 = -5/4+9/4

x^2-3x+9/4 = 1

(x-3/2)^2 = 1

Apply squre root on each side.

x-3/2 = ±1

Add 3/2 to each side.

x = ±1+3/2

x = 1+3/2 and -1+3/2

x = 5/2 and 1/2

Roots are x = 5/2

x = 1/2.