Question

X^2 + 10x + 21 = 0

Solve for x using "Completing the Square"

Answer 1

x= -3 & -7 to the quadratic equation!

Answer 2

`x=-7,-3`

Explanation:

Completing the square means you are changing the polynomial so that it is a perfect square trinomial. Since the middle term is 10, we need the last term to be 25 since 5+5=10, thus, 5*5=25:

`x^2+10x+21=0\\x^2+10x+21+4=0+4\\x^2+10x+25=4\\(x+5)^2=4\\x+5=\pm2\\x=-7,-3`

As you can see, because we change
`x^2+10x+21` to
`x^2+10x+25` by adding 4 to both sides, we were able to reduce it to
`(x+5)^2`, a perfect square, and solve the rest of the problem.