what is the answer to 4x^2 -39x+56=0 when completing the sqaure?

Question

solve this equation by completing the square.

Answer 1

4x^2-39x+56 = 0

Separate variables and constants aside by subtracting 56 from each side.

4x^2-39x= -56

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

x^2-(39/4)x = -14

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

x^2-(39/4)x+1521/64 = -14+1521/64

(x-39/8)^2 = 625/64

Apply squre root on each side.

x-39/8 = ±25/8

Add 39/8 to each side.

x = 25/8+39/8 and x = -25/8+39/8

x = 64/8 and x = -14/8

x = 8 and x = -1.75

Roots are x = 8

x = -1.75.

 

Comments

x = 25/8 + 39/8 and x = - 25/8 + 39/8

x = 64/8 and x = 14/8

x = 8 and x = 7/4

The roots are x = 8 and x = 7/4.