Question

x^(2)+18x+79=0
solve the quadratic equation by completing the square.

Answer 1

Do you know how to complete the square? Basically what you are trying to do is that you have to find something an expression like x + 2 or something, that when you square, contains that x^2 + 18x part in it. When it contains that, you can simply add or subtract whatever you need to in order to equalise the constant at the end.

For example, if I have the function x^2 + 4x - 30 = 0 given to me and I have to complete the square, then I find something that when I square it, I get the "x^2 + 4x" part in it. So from what I know, squaring x + 2, will give me that x^2 + 4x in it. So it goes like this:

(x + 2)^2 + k = x^2 + 4x - 30
x^2 + 4x + 4 + k = x^2 + 4x - 30
x^2 + 4x + 4 - 34 = x^2 + 4x - 30
(x + 2)^2 - 34 = x^2 + 4x - 30

So you see what I did there? I found something that when squared, contains the part of the equation that I want, but then to make the constant the same, I have to add a value k to the other side in order to make the constants the same on both sides. That's basically completing the square. @jmprz_793