Assuming x2 - 19x + 20 = 0, find the possible values of x using factorization method.
Solution.
x2 + 19x - 20 = 0
Step1
Find two numbers which, when multiplied will give the constant term (ie -20) and when added (or subtracted) will give the coefficient of x (ie +19)
Factors: factors of -20 are
-20 and +1 (-20 x 1 = -20; -20 + 1 = -19. This does not satisfy the equation)
+20 and -1 (20 x -1 = -20; 20 - 1 = 19. This satisfies the equation)
Step2
Replace -19x with x and -20x in the equation. (Note that x is the same as 1x)
We then have x2 + x - 20x - 20 = 0 (by splitting -19x into x and -20x)
Step3
Group the first two terms together and the last two terms together as follows
x2 + x - 20x - 20 = 0
By bringing out common terms, this becomes
x(x + 1) - 20(x + 1) = 0
note that 1 in the bracket now has a + sign such that when multiplied by the – sign outside the bracket, the result will still be minus
Since the two brackets are the same, we take one of them and multiply by the coefficients of the brackets as follows
(x + 1)(x - 20) = 0
If two things are multiplied and the result is zero, it means that either one of them is equal to zero or both are equal to zero
Therefore,
Either x + 1 = 0, which gives x = 0 – 1
And therefore x = –1
Or x - 20 = 0, which gives x = 0 + 20
And therefore x = 20
The values of x that satisfy the equation
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