Question

In the following exercise, solve by completing the square.

$u^2+2u=3$

Short answer

The required solution is$u=1$.

Step-by-step solution

Step 1. Given Information

We are given the quadratic equation

$u^2+2u=3$

Step 2. Calculation

$u^2+2u=3$

$\Rightarrow u^2+2u+{\left(\frac{2}{2}\right)}^2=3+{\left(\frac{2}{2}\right)}^2$ take half of $2$, square it and add it to both sides

$\Rightarrow u^2+2u+1=4$

$\Rightarrow {(u+1)}^2=4$ write it as binomial squared

$\Rightarrow u+1=2$ take square root on both sides

$\Rightarrow u=1$ simplify