Question

Find a solution to the equation. x^2-6x+8=0

Answer 1

x=4, x=2

Explanation:

Pre-Solving

We are given the equation x² - 6x + 8 = 0

We want to find a solution to the equation.

This is a quadratic trinomial, which can be solved by factoring.

Solving

Factoring a quadratic trinomial will give us two binomials, which are multiplied together.

For a quadratic trinomial, it will factor into (x+a)(x+b). a and b are two numbers that when added together, create the middle coefficient (in this case, -6), and when multiplied, create the third term (in this case, 8).

So think: what two numbers add up to -6, but multiply to 8?

Those numbers are -4 and -2.

So, substitute -4 and -2 as a and b.

(x-4)(x-2)

Recall that x²-6x+8 was equal to 0. Its factored form is also equal to 0.

(x-4)(x-2)=0

Via zero product property, as long as either one of the binomials equals 0, the entire thing will equal 0.

So, we can split this into two equations:
x-4 = 0 and x-2= 0

This gives us two solutions: x=4, and x=2, and either one will work to make the entire thing 0.

Answer 2

The equation is given as,

`x^2-6x+8=0`

Factorizing the given equation,

`\begin{gathered} x^2-6x+8=0 \\ x^2-4x-2x+8=0 \\ \end{gathered}`

Taking common terms out of the bracket,

`\begin{gathered} x\left(x-4\right)-2\left(x-4\right)=0 \\ (x-4)(x-2)=0 \end{gathered}`

Therefore the value of x is calculated as,

`\begin{gathered} x-4=0\text{ and x-2 = 0} \\ x\text{ = 4 and x = 2} \end{gathered}`

Thus the solution of the given equations are 2 and 4.