# Math Help - Finding values of quadratic equation

1. ## Finding values of quadratic equation

Got a math sum I'm working on thats troubling me.

${x}^{2} + 4x - 8$ can be written in the form ${(x + p)}^{2} + q$

Find the values of $p$ and $q$

2. Originally Posted by yorkey
Got a math sum I'm working on thats troubling me.

${x}^{2} + 4x - 8$ can be written in the form ${(x + p)}^{2} + q$

Find the values of $p$ and $q$
You have two options, both require that you have the necessary knowledge and understanding.

Option 1: Complete the square for x^2 + 4x - 8 and compare with (x + p)^2 + q.

Option 2: Expand (x + p)^2 + q and equate the coefficients of the various powers of x with the corresponding coefficients in x^2 + 4x - 8.

3. Ok great! Thanks

p = 2
q = -8

Does that work?

4. ${(x + 2)}^{2} - 8= x^2+2x+2x+4-8= x^2+4x-4$.

So p looks correct, but q does not. You almost got it though.

5. Oh I'm a retard. My reasoning went something like this:

(x + 2)^2 is expanded to x^2 + 4, which it obviously is NOT. So q is -12, right?

6. Originally Posted by yorkey
Oh I'm a retard. My reasoning went something like this:

(x + 2)^2 is expanded to x^2 + 4, which it obviously is NOT. So q is -12, right?
Hi yorkey,

Yes, q = -12

Complete the square on $x^2+4x+4$

$(x^2+4x\: {\color{red}+4})-8 \: {\color{red}-4}$

$(x \: {\color{red}+2})^2\: {\color{red}-12}$

7. Y'all are legends, thanks.

/this case is closed