Question

Solve ( X -1)^2-80 = zero , where x is a real number simplify your answer as much as possible

Answer 1

We are given the following equation

`(x-1)^2-80=0`

Let us solve the above equation.

Add 80 to both sides of the equation

`\begin{gathered} (x-1)^2-80+80=80 \\ (x-1)^2=80 \end{gathered}`

Take square root on both sides of the equation

`\begin{gathered} √((x-1)^2)=√(80) \\ x-1=\pm\sqrt[]{80} \end{gathered}`

Add 1 to both sides of the equation

`\begin{gathered} x-1+1=\pm\sqrt[]{80}+1 \\ x=1\pm\sqrt[]{80} \end{gathered}`

So, there will be two solutions

`x=1+\sqrt[]{80}\; \; and\; \; x=1-\sqrt[]{80}`

Simplify the root

`x=1+4\sqrt[]{5}\; \; and\; \; x=1-4\sqrt[]{5}`

Therefore, the solution of the given equation is

`x=1+4\sqrt[]{5},\; 1-4\sqrt[]{5}`