Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 4x2 + 2x + 4 = 0

Question

Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 4x^2+2x+4=0

Answer 1

x² + 0.5x + 1 = 0; x² + 0.5x + 0.0625 = - 1 + 0.0625; (x + 0.25)² = - 0.9375

Answer 2

4x^2 + 2x +4 = 0

discriminant = b^2-4ac = 4-64<0, so there's no real solution

x^2 +x/2 =-1

x^2 +x/2 + 1/16 =-1 +1/16

(x+1/4)^2 = -15/16

x+ 1/4 = + or - (1/4)isqr15

x = (-1+isqr15)/4, (-1-isqr15)/4) two imaginary solutions

(x+p)^2 =q

x+p = + or - q

x = -p+ or -q

x = -p-q or -p+q