For example: ax 2+bx+c = 0.
Step 1: put forward the coefficient of quadratic term: a [x 2+(b/a) x]+c = 0. Regardless of the constant term;
Step 2: Divide the coefficient of the first term by "2"; a[x^2+(b/2a)x]+c=0
Step 3: change the unknown term into a complete square form: a (x+b/2a) 2-a * (b 2/4a2)+c = 0;
That is, a (x+b/2a) 2-b 2/4a+c = 0. -B2/4a- is the term added to the square and must be subtracted; If the second item after the formula is preceded by "-",add the subtracted item!
Step 4: Merge constant terms: a (x+b/2a) 2-(b 2-4ac)/4a = 0.
Step 5: Move the constant term to the right of the equal sign and divide both sides by the coefficient a (a ≠ 0) of the quadratic term;
(x+b/2a)^2=(b^2-4ac)/4a^2；
Step 6: square the two sides; x+b/2a = √(b^2-4ac)/2a；
Step 7: X: X =-b/2a √ (b 2-4ac)/2a is obtained.
x=[-b √(b^2-4ac)]/2a.
X 1 takes "+",X2 takes "-",and vice versa.
Generally speaking, there should be two root causes, but the specific situation should be analyzed in detail. For example, if x represents the length and area of a specific object, negative values should be removed and only positive values should be taken.
The collocation method is very long to write, but it is clear and convenient when you are skilled. I wish you progress in your study!