Thank you for the help Use the completing the square techniq

Thank you for the help!

Use the \"completing the square\" technique to solve for x in the equation ax^2 + bx + c = 0, thus proving the quadratic formula: x = -b plusminus squareroot b^2 - 4ac/2a.

Solution

ax^2 + bx + c =0

a( x^2 +(b/a)x ) + c =0

Making term inside perfect sqaure :

a(x^2 + (b/a)x + b^/4a^2 - b^2/4a^2) +c =0

a(x + b/2a)^2 -b^2/4a + c=0

a(x+b/2a)^2 = b^2/4a - c

(x+ b/2a)^2 = b^2/4a^2 - c/a

Taking sqaure root on both sides:

(x+ b/2a) = +/- sqrt[ b^2 - 4ac]/2a

x = - b/2a +/- sqrt[ b^2 - 4ac]/2a