Question

When solving x2 + 10x + 3 = 0 by completing the square, which of the following is a step in the process?

Answer 1

`x^2+10x+3=0`

Group terms containing x:

`\begin{gathered} (x^2+10x+_{\text{ -}})+3-_{\text{ -}}=0 \\ \end{gathered}`

Take one half of the coefficient of x and square it:

`\begin{gathered} (x^2+10+25)+3-25=0 \\ \end{gathered}`

The factors of 25 which sum to 10 are 5 and 5 so:

`\begin{gathered} x^2+10+25=(x+5)(x+5)=(x+5)^2 \\ so\colon \\ (x+5)^2=22 \end{gathered}`

Answer:

`(x+5)^2=22`