Solve quadratic equation x2 + 7x + 12 = 0

(a) First: take take co-efficient of x2 term which here is 1;
(b) Then: take take the last term or constant term which here is +12;

Multiply +1 and +12, which gives +12

Now, we need to find two factors of +12. THESE FACTORS HAVE TO SATISFY TWO CONDITIONS.

1st condition: when we multiply those factors, we should get +12 and;

2nd condition: when we add those factors, we should get +7

Upon deep thinking, we calculate and get the factors as +4 and +3.

So, we get the two factors as +4 and +3

IMPORTANT: So, it means that we can split the middle term of given quadratic equation into these two numbers +4 and +3.

Now we can split the given middle term (+7x) and rewrite the quadratic equations as x2 + 4x + 3x + 12 = 0

Now we need to group the terms as shown by the coloured boxes.

Take common from the first bracket: Here 'x' is present in both the terms. So, we take 'x' common as shown in the figure.

Take common from the second bracket: Here '3' is present in both the terms. So, we take '3' common as shown in the figure.

We see that (x + 4) is appearing twice. It means that (x + 4) is the common term. So we take it out common and write the other two terms 'x' and '3' in bracket.

We see that the RHS is zero. LHS is a multiplication of two brackets. In mathematics, multiplication of any number with zero will give zero That meamsn any of the two brackets can be zero. So, we take both the brackets and equate them to zero.

Solving these equations, we get the final answer of the quadratic equation as x = -4 or x = -3. That means that the variable 'x' can have the value as -4 or -3.