Question

How to solve a quadratic equation by completing the square

Answer 1

let us take an example to solve it

3x²+4x-7=0
it is in the form of ax²+bx+c=0

STEP 1: First divide the equation with a=3
x²+4x/3-7/3=0

STEP 2: Now add and subtract (2/3)²
[x²+4x/3+(2/3)²]-(2/3)²-7/3=0

STEP 3: then take the coefficient on RHS and solve the equation
(x+2/3)²=4/9+7/3
(x+2/3)²=4+21/9
(x+2/3)²=25/9
x+2/3=±√(25/9)
x+2/3=±5/3
so,
x=5/3-2/3=3/3=1
and
x=-5/3-2/3=-7/3
so, x=1,-7/3

Answer 2

i think it can be solve by doing this:-

Step 1 Divide all terms by a (the coefficient of x²).

Step 2 Move the number term (c/a) to the right side of the equation.

Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation