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
