Question

How do you solve ${x^2}$ - 6$x$ + 8 = 0?

Answer 1

Hint: Use middle term splitting formula and then find the common factors for the equation.

Complete step-by-step answer:
Given the quadratic equation as ${x^2}$ - 6$x$ + 8 = 0
So we will use middle term splitting here.
Here middle term is - 6$x$
We need to factorize this term to get two numbers whose sum will be -6 and product will be 8
Here 8 should come from the product of ${x^2}$ coefficient and the constant.
So we can write the given equation as
=>${x^2}$ - (4+2)$x$ + (4x2) = 0
=>${x^2}$ - 4$x$- 2$x$ + (4x2) = 0
=>\[({x^2} - 4x)\] - $(2x - 8)$= 0
Taking common from each term (factor each binomial)
=>\[x(x - 4)\] - $2(x - 4)$ = 0
Now factor out common factors which is $(x - 4)$
=>\[(x - 4)\] $(x - 2)$ = 0
Therefore, the factors for the equation ${x^2}$ - 6$x$ + 8 = 0 will be \[(x - 4)\] $(x - 2)$
and x = 4, 2

Note: We can also verify the factors by putting the values in the equation. For example-
Let’s check for 2
${x^2}$ - 6$x$ + 8 = 0, putting 2 in place if x then L.H.S. should be 0
=>${2^2}$ - (6x2) + 8
=>4 -12 + 8
=>8 – 8
=>0
It means 2 is correct factor the above equation ${x^2}$ - 6$x$ + 8 = 0