Derive the quadratic formula form the general quadratic equation

Write the general quadratic equation : ax²+bx+c = 0 Need to solve for 'x' using completing the square method. 1 - Divide through by 'a' in order to get into a form which we can complete the square of : x²+bx/a+c/a=0. 2 - Explain about completing the square and since (a+b)²=a²+b²+2ab, (x+b/2a)²=x²+b²/4a²+bx/a . Therefore (x+b/2a)²-b²/4a²+c/a=03 - Rearrange to get all the 'x' terms on one side as we're solving for x:(x+b/2a)²=b²/4a²-c/a . 4 - LHS: Make denominator same for both fractions and add the fractions: (x+b/2a)²=b²/4a²-4ac/4a² (x+b/2a)²=(b²-4ac)/4a² . 5 - Square root both sides and simplify: x+b/2a=+_sqrt((b²-4ac)/4a²) x+b/2a=+_sqrt(b²-4ac)/sqrt(4a²) x+b/2a=+sqrt(b²-4ac)/2a6 - Rearrange for 'x' and simplify: x = (-b/2a)+(sqrt(b²-4ac)/2a) x = (-b+_sqrt(b²-4ac))/2a