Question

Find the solution of the quadratic equation ax²+bx+C=0 by completing square method

Answer 1

Follow these steps:

1) Set the constant in the first term equal to 1 by dividing both sides by a:

x²+b/ax+C/a=0

2) Rearrange the equation by subtracting C/a to both sides of the equal sign:

x²+b/ax=-C/a

3) Take 1/2 the second term constant, square it, and add it to both sides.

x²+b/ax+b2/4a2=-C/a+b2/4a2

4) Note that the expression x²+b/ax+b2/4a2 can be factored as a square

(x+b/a)(x+b/a) = (x+b/a)2 = -C/a+b2/4a2

5) Take the square root of both sides of the equation, remembering that the result can be a positive (+) number or a negative (−) number:

(x+b/a) = +- sqrt b2/4a2-C/a

6) Subtract b/a to both sides to get your answer:

x = +- sqrt b2/4a2-C/a-b/a

Hope this help!