Question

In the following exercise, solve by completing the square.

$x^2-20x=21$

Short answer

The required solution is$x=21$.

Step-by-step solution

Step 1. Given Information

We are given the quadratic equation

$x^2-20x=21$

Step 2. Calculation

$x^2-20x=21$

$\Rightarrow x^2-20x+{\left(\frac{20}{2}\right)}^2=21+{\left(\frac{20}{2}\right)}^2$ take half of $20$, square it and add it to both sides

$\Rightarrow x^2-20x+100=21+100$

$\Rightarrow x^2-20x+100=121$ simplify

$\Rightarrow {(x-10)}^2={11}^2$ write it as binomial squared

$\Rightarrow x-10=11$ take square root on each side

$\Rightarrow x=21$ simplify