Question

Quadratic Factoring: Demonstrate solving some quadraticequations using the following methods: factoring, taking theroot, and completing the square.

Answer 1

The Solution:

Let's solve with the Factoring Method:

`x^2-x-6=0`
`\begin{gathered} x^2-3x+2x-6=0 \\ x(x-3)+2(x-3)=0 \\ (x+2)(x-3)=0 \end{gathered}`
`\begin{gathered} x+2=0\text{ or }x-3=0 \\ x=-2\text{ or }x=3 \end{gathered}`

Solving by the Completing the Square:

`\begin{gathered} x^2-x=6 \\ x^2-x+((1)/(2))^2=6+(1)/(4) \\ \\ (x-(1)/(2))^2=(25)/(4) \end{gathered}`

Take the square root of both sides.

`\begin{gathered} x-(1)/(2)=\sqrt{((25)/(4))} \\ \\ x=(1)/(2)\pm(5)/(2)=(1\pm5)/(2) \end{gathered}`
`\begin{gathered} x=(1+5)/(2)=(6)/(2)=3 \\ \\ \\ x=(1-5)/(2)=(-4)/(2)=-2 \end{gathered}`

Therefore, the answers is:

`x=-2\text{ or }x=3`