complete the square to solve the equations below

Question

x^2 + x = 19 / 4

Answer 1

The equation is x² + x = 19/4

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

 Here x coefficient = 1. so, (half the x coefficient)² = (1/2)²= 1/4.

Add 1/4 to each side.

x² + x + 1/4 = 19/4 + 1/4

(x + (1/2))² = 20/4.

(x + (1/2))² = 5.

x + (1/2) = ± 5

 

x + (1/2) =  5

x + (1/2) -(1/2) =  5 -(1/2)

x = 9/2

 

x + (1/2) = - 5

x + (1/2) -(1/2) = - 5 -(1/2)

x = -11/2

 

So solutions are 9/2 and -11/2