Question

Solve${(x-2)}^2+1=37$. Describe the steps you use.

Short answer

The solution of equation is$x=8,-4$.

Step-by-step solution

Step 1. Given Information.

The given equation is${(x-2)}^2+1=37$.

Step 2. Calculation.

The expression can be solved as

$\begin{array}{c}{(x-2)}^2+1=37\\ {(x-2)}^2=37-1\\ x^2+4-4x=36\\ x^2-4x-32=0\end{array}$

On further simplification,

$\begin{array}{d}{x}^2-8x+4x-32=0\\ x(x-8)+4(x-8)=0\\ (x-8)(x+4)=0\\ x=8,-4\end{array}$

Step 3. Conclusion.

The solution of equation is$x=8,-4$.