Question

$x { }^{2} - 7x + 12 = 0$
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Answer 1

Answer :

(in the attachment)

Steps followed :

1. First weight of the given numbers and try to split the middle term .
2. Then according to splitting the middle term the number in the centre must be the addition or subtraction of two numbers . And the constant term must be the multiplication of same two numbers.
3. In symbolic form it can be written as P×Q = 12 and P+Q = 7x
4. When we find out the factors of 12 we find that 3 + 4 is exactly 7 and 3 × 4 is 12
5. So we took the numbers in the middle as common terms.
6. Then divided the terms into two parts two from the right and two from the left.
7. Then took the common terms and simplified them .

(x-3)(x+4)

Note as 0 doesn't have any value excluding it in the answer mostly doesn't matter

Answer 2

x^2 - 7x + 12 =0
It implies that the given equation can be written as,
x^2 - 3x - 4x +12 =0
x(x-3) -4(x-3) =0
Using zero product rule,
(x-4)(x-3)=0
It implies that x can either be 3 or 4