Question

Solve the quadratic equation by completing the square and applying the square root property.

u2 + 20u + 101 = 0

Answer 1

`u = - 10 + i, \: \: - (10 + i)`

Explanation:

`{u}^(2) + 20u + 101 = 0 \\ \\ \implies \: {u}^(2) + 20u + 100 + 1 = 0 \\ \\ \implies \: {u}^(2) + 20u + {(10)}^(2) + 1 = 0 \\ \\ \implies \: {(u + 10)}^(2) = - 1 \\ \\ \implies \: {u + 10} = \pm√( - 1) \\ \\ \implies \: {u} = \pm \: i - 10\\ \\ u = i - 10 \: \: or \: \: u = - i - 10 \\ \\ u = i - 10 \: \: or \: \: u = - (10 + i) \\ \\ u = - 10 + i, \: \: - (10 + i)`

Answer 2

Answer: u = -10 + i or u = -10 - i

Explanation:

`\begin{aligned}&u^(2)+20 u+101=0 \\&u^(2)+10^(2)+2 * 10 * 6 u+101-1000=0 \\&(u+10)^(2)=-1\end{aligned}`

`\begin{aligned}&u+10=\pm √(-1) \\&u+10=\pm i \\&u=-10 \pm i \\&\bold{u=-10+i \quad \text { or } u=-10-i}\end{aligned}`