completing the square

Question

x^2+x=-7/4.

Answer 1

Given equation x^2+x = -7/4

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.

x^2+x+1/4 = -7/4+1/4

(x+1/2)^2 = -3/2

Apply squre root on each side.

x+1/2 = ±√(3/2)i^2

x+1/2 = ±√(3/2)i

Subtract 1/2 from each side.

x+1/2-1/2 = -1/2±√(3/2)i

x = -1/2±√(3/2)i

Roots are x = -1/2+√(3/2)i

x = -1/2-√(3/2)i