Question

A. Find the solutions of the following quadratic equations using the method specified on each item. (3 pts, each) x²-8x+12=0 3. x²-6x-7=0 (use factoring) (use completing the squarel

Answer 1

For x²-8x+12=0, we have:

`x^2-8x+12=0`

Factoring the expression:

`\begin{gathered} \left(x^2-2x\right)+\left(-6x+12\right)=0 \\ x(x-2)-6(x-2)=0 \end{gathered}`

Factor the common term x - 2:

`(x-2)(x-6)=0`

Separate the solutions:

`\begin{gathered} x-2=0 \\ x-2+2=0+2 \\ x=2 \\ and \\ x-6=0 \\ x-6+6=0+6 \\ x=6 \end{gathered}`

Answer: x = 2 and x = 6

For x²-6x-7=0, we have:

`x^2-6x-7=0`

Factor the expression:

`\begin{gathered} \left(x^2+x\right)+\left(-7x-7\right)=0 \\ x(x+1)-7(x+1)=0 \end{gathered}`

Factor x + 1:

`(x+1)(x-7)=0`

The solutions are:

`\begin{gathered} x+1=0 \\ x+1-1=0-1 \\ x=-1 \\ and \\ x-7=0 \\ x-7+7=0+7 \\ x=7 \end{gathered}`

Answer: x = -1 and x = 7