Question

Completing the square to find the zeros 4. a-2a-8=0

Answer 1

a = -2

a = 4

Step-by-step explanation:

We add 8 to both sides to get

`a^2-2a=8`

adding 1 to both sides completes the square on the left to give

`\begin{gathered} a^2-2a+1=8+1 \\ (a-1)^2=9 \end{gathered}`

We now take the square root of both sides to get

`\begin{gathered} \sqrt[]{(a-1)^2}=\sqrt[]{9} \\ a-1=\pm3 \end{gathered}`
`a=\pm3+1`

which gives us two solutions

`\begin{gathered} a=3+1=4 \\ a=-3+1=-2 \end{gathered}`

Hence, the zeros of the equation are a = 4 and a = -2.