Question

Complete the square on the following quadratic x2+10x+9=0

Answer 1

Given a quadratic equation
`x^(2) +ax+c=0`

1. the first thing we do when we want to compete the square, is write the coefficient of x as 2 times a number.

In our case the coefficient of x is 10, so we write 10 as 2*5

2. then we write +
`5^(2)` and -
`5^(2)` to the expression:


`x^(2) +2*5*x+ 5^(2) -5^(2)+9=0`


`(x^(2) +2*5*x+ 5^(2)) -25+9=0`


`(x+5)^(2)-16=0`



Answer:
`(x+5)^(2)-16=0`