Question

If using the method of completing the square to solve the quadratic equationX2 + 15x + 7 = 0, which number would have to be added to "complete thesquare"?

Answer 1

225/4

Step-by-step explanation

To complete the square we want to write a part of the equation in the form:

`(a+b)^2=a^2+2ab+b^2`

The second term squared is the one we have to add to the equation in order to complete the square.

In this case, the coefficient of x is 15, so b is:

`b=(15)/(2)`

And b²:

`b^2=(225)/(4)`

If we add 225/4 to both sides of the equation:

`x^2+15x+(225)/(4)+7=(225)/(4)`

We complete the square:

`(x+(15)/(2))^2+7=(225)/(4)`